Find the general solution to the homogeneous differential equation...
Question:
Find the general solution to the homogeneous differential equation {eq}\frac{d^2y}{dt^2}-15\frac{dy}{dt}=0 {/eq}.
Homogeneous Differential Equation
Consider the following homogeneous second-order differential equation
{eq}\displaystyle f(t)y'' + g(t)y' = 0 \quad (*) {/eq}
Then, equation (*) can be solved by making the following substitutions
{eq}\displaystyle u = y' \Rightarrow u' = y'' {/eq}
So that equation (*) becomes the following separable differential equation
{eq}\displaystyle f(t)u' + g(t)u = 0 {/eq}
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answerLet
{eq}\displaystyle v = \frac{dy}{dt} \quad (1) \\ \\ \displaystyle \Rightarrow \frac{dv}{dt} = \frac{d^2y}{dt^2} \quad (2) {/eq}
Using...
See full answer below.
Ask a question
Our experts can answer your tough homework and study questions.
Ask a question Ask a questionSearch Answers
Learn more about this topic:
Get access to this video and our entire Q&A library
Separable Differential Equation: Definition & Examples
from
Chapter 16 / Lesson 1
6.7K
Discover what separable differential equations are and their uses. Learn to identify if an equation is separable and how to solve them through given examples.
Related to this Question
- Find the general solution to the homogeneous differential equation: y" - 8y' + 25y = 0.
- Find the general solution to the homogeneous differential equation. y''' - y = 0.
- Find the general solution to the following homogeneous differential equation: y'' + 2y' + 2y = 0
- Find the general solution to the homogeneous differential equation d2y/dx2 - 5dy/dx + 4y = 0
- Find the general solution to the homogeneous differential equation. 4y'' + y' = 0.
- Find the general solution of the homogeneous differential equation y'' -4y' + 4y = 0
- Find the general solution of the homogeneous differential equation \frac{d^2y}{dt^2} + 10\frac{dy}{dt} + 25y = 0
- Find the general solution of the homogeneous differential equation y'=x+y x-y .
- Find the general solution to homogeneous differential equation: (y^2 + y x) dx + x^2 dy = 0
- Find the general solution to the homogeneous differential equation d^2y dt^2 -5dy dt =0.
- Find the general solution of the homogeneous differential equation. \\ y'' - 7y' + 10 y = 24e^x
- Find the general solution for the following homogeneous differential equation. 3 x dy / dx - 3 y = 4 x sec (y / x)
- Find the general solution of the homogeneous differential equation y'' + 2y' + 5y = 0.
- Find the general solution to the homogeneous differential equation. \frac{d^2y}{dt^2} - 16 \frac{dy}{dt} + 68y = 0.
- Find the general solution of the homogeneous differential equation y'' + 1y = 0
- Find the general solution to the homogeneous differential equation \frac { d ^ { 2 } y } { d t ^ { 2 } } - 16 \frac { d y } { d t } + 164 y = 0.
- Find the general solution to the homogeneous differential equation: 12y" - 11y' - 5y = 0.
- Find the general solution to the following homogeneous differential equation: y''' + y' = 0.
- Find the general solution to the homogeneous differential equation (d^2 y)/(dx^2) + 3(dy/dx) - 4y = 0.
- Find the general solution of the homogeneous differential equation y'' + 7y' + 10y = 0
- Find the general solution to the homogeneous differential equation: (d^2 y)/(dt^2) - 8 dy/dt + 20y = 0.
- Find the general solution to the homogeneous differential equation \frac{d^2y}{dt^2} -0\frac{dy}{dt} + 0y= 0
- Find the general solution to the homogeneous differential equation: d^2y dx^2 -9dy dx -10y=0.
- Find the general solution to the homogeneous differential equation \frac{d^2y}{dt^2} - 8\frac{dy}{dt} + 16y = 0
- Find the general solution to the homogeneous differential equation: (d2y/dt2)+10(dy/dt)+24y=0
- Find the general solution of the non homogeneous differential equation y'' -4y' + 4y = 2e^{2x} + 4x -12
- Find the general solution to the homogeneous differential equation: \frac{d^2y}{dx^2} - 22 \frac{dy}{dx} + 117y = 0
- Find the general solution of the differential equation. Homogeneous: (x - y)y' = x + y
- Find the general solution to the homogeneous differential equation \frac{d^2y}{dt^2}-20\frac{dy}{dt}+125y=0. The solution has the
- Find the general solution to the homogeneous differential equation \frac{d^2 y}{dt^2} - 18 \frac{dy}{dt} + 130y = 0 The solution has the form y = C_1 f_1 (t) + C_2 f_2 (t) Left to your own devices
- Find the general solution to the homogeneous differential equation d^2y/dt^2 - 5dy/dt = 0. The solution has the form y = C_1f_1(t) + C_2f_2(t).
- Find the general solution to the homogeneous differential equation frac{d^2y}{dt^2} - 8 frac{dy}{dt} + 32y = 0 The solution has the form y = C_1 f_1(t) + C_2f_2(t) with f_1(t) = ? and f_2(t)
- Find the general solution to the non-homogeneous differential equation y''+y'-6y=sinx
- Find the general solution to the non-homogeneous differential equation. 2 x^2 {d^2y} / {dx^2} - 10 x {dy} / {dx} - 14 y = 8 cos (3 x)
- Determine whether the given differential equation is homogeneous, and if so find the general solution. x(x + y)y' = y(x-y)
- Find the general solution to the homogeneous differential equation: \\ \frac{d^2y}{dt^2}-6\frac{dy}{dt}+18y=0
- Find the general solution to the homogenous differential equation y 8 y + 25 y = 0
- Find the general solution to the homogeneous differential equation (d^2y)/(dx^2) +5 dy/dx + 6y = 0. The solution has the form y = C_1 f_1(x) + C_2 f_2(x). Find f_1(x) and f_2(x).
- Find the general solution to the homogeneous differential equation \frac{d^2y}{dt^2} - 9 \frac{dy}{dt} + 14y = 0 The solution can be written in the form y = C_1 e^{r_1t} + C_2 e^{r_2t} with r_1 < r_2
- Find the general solution to the homogeneous differential equation d 2 y/ d t 2 - 6 d y d t + 9 y = 0 . The solution can be written in the form y = C 1 f 1 ( t ) + C 2 f 2 ( t )
- Find the general solution to the homogeneous differential equation d^2 y / d t^2 - 6 d y / d t = 0. The solution can be written in the form y = C_1 e^{r_1 t} + C_2 e^{r_2 t} with r_1 less than r_2 Usi
- Find the general solution to the homogeneous differential equation \frac{d^2y}{dt^2}+6\frac{dy}{dt}+9y=0 The solution can be written in the form
- Find the general solution to the homogeneous differential equation ({d^2}y)/({dt}^2) - 1({dy)/({dt}) = 0. The solution can be written in the form y = C_1 e^{r_1 t} + C_2 e^{r_2 t} with r_1 < r_2. Usin
- Find the general solution to the homogeneous differential equation {d^2y}{dt^2}-4 {dy}{dt}+4y=0.
- Show that the differential equation dy/dx = (3y^2 + 10x^2)/(xy) is homogeneous. Then find the general solution.
- Find the general solution of the given non-homogenous differential equation: y'' + 4y = 1 + x + x^2
- Find the general solution of the given non-homogenous differential equation: y'' - 5y' + 6y = 5e^{-2x}
- Find the general solution to the homogeneous differential equation d^2 y / dt^2 + 10 dy / dt + 25 y = 0 The solution can be written in the form y = C_1 f_1 (t) + C_2 f_2 (t). Find f_1 (t) and f_2 (t).
- Find the general solution to the homogeneous differential equation { \frac{d^2y}{dt^2} - 16\frac{dy}{dt} + 145y = 0 } The solution has the form { y=C_1f_1(t) + C_2f_2(t) \\with, f_1(t) =...........
- Find the general solution to this homogeneous differential equation: dy dx = x+y x-y .
- Find the general solution of the homogeneous differential equation x(x + y)\frac{dy}{dt} = y (x - y). Leave the answer in implicit form.
- Find the general solution of the homogeneous differential equation: x(x + y) dy/dx = y(x - y). Leave your answer in implicit form.
- 1. Find the general solution to the homogenous differential equation \dfrac{d^2y}{dt^2}+20\dfrac{dy}{dt}+100y=0 2. The solution can be written in the form y=C_1f_1(t)+C_2f_2(t) with f_1(t) = {Blank} a
- a) Find a particular solution to the non homogeneous differential equation y'' + 4y' + 5y = -5x +5e^{-x} b) Find the most general solution to the associated homogeneous differential equation. c)
- Find the solution to the homogeneous differential equation 2 \frac{d^2y}{dx^2} + \frac{dy}{dx} - y = 0.
- (a) Find a particular solution to the nonhomogeneous differential equation y ?? + 4 y ? + 5 y = ? 5 x + 5 e ? x . y p = _____ (b) Find the most general solution to the associated homogeneous diffe
- Find a linear homogeneous differential equation with the general solution y=c1+c2e^2x+c3e^{-5}x
- Find the general solution to the homogeneous differential equation d^2 y/dt^2 - 20 dy/dt + 100y = 0. Write the solution in the form y = C_1 f_1(t) + C_2 f_2(t).
- 1. Find a particular solution to the nonhomogeneous differential equation y" + 3y' - 4y = e^(5x) 2. Find the most general solution to the associated homogenous differential equation. Use c_1 and c
- (a) Find a particular solution to the nonhomogeneous differential equation y ?? + 4 y ? + 5 y = 10 x + 3 e ? x . (b) Find the most general solution to the associated homogeneous differential equatio
- Find the general solution to the homogeneous second-order differential equation. y'' - 4y' + 13y = 0
- Find the general solution to the homogeneous second-order differential equation. 12y'' - 11y' - 5y = 0
- Find the general solution to the homogeneous second-order differential equation. 8y'' - 2y' - 3y = 0
- Find the general solution to the homogeneous second-order differential equation: y" - 8y' +25y = 0.
- Find the general solution of the differential equation by the method of homogenous substitution. (x^2-y^2)y' = 2xy
- Consider the differential equation {x^2}y'' - xy' + y = x(8 + {1/ln(x)}). (A) Find the general solution of the related homogeneous differential equation. (B) Find the general solution of the non-homog
- Find a particular solution to the non homogeneous differential equation y'' + 4y' + 5y = -10x + 3e^{-x}
- Find a particular solution to the non homogeneous differential equation y'' + 4y' + 5y = -5x + e^{-x}
- Find the general solution of the nonhomogeneous differential equation y'' + y = 4 \cos x.
- Find the general solution for the nonhomogeneous differential equation: y" + 3y' - 10y = 6e(2x)
- Find the general solution of the nonhomogeneous differential equation y''+y'-12y = 2x
- Find a general solution to the nonhomogeneous differential equation \hspace{10mm} y''-2y'+y=e^t \tan ^{-1} t
- a. Find a particular solution to the non-homogeneous differential equation y'' + 4y' + 5y = 10x + 5e^{-x}. b. Find the most general solution to the associated homogeneous differential equation. (Use
- Find a particular solution for the homogeneous differential equation given below. -y^2 dx + x(x + y) dy = 0, y(1) = 1.
- Find the general solution to the homogeneous differential equation \frac {d^2 y}{dt^2} - 12 \frac {dy}{dt} + 52y = 0 The solution has the form y = C_1 f_1 (t) + C_2 f_2(t)
- Find the general solution of the homogeneous differential equation {y}' = \frac{x + y}{x - y}.|, u = \frac{y}{x}| then u| satisfies the DE x \frac{du}{dx} + u = | Separate variables to get du = | dx|
- Find the general solution of the differential equation. d^4y over dx^4 - y = 6e^- x
- Find the general solution to the differential equation. x_1 t is a solution to the differential equation t^2 x''+ 3tx' -3x = 0, x1 t = t
- Find the general solution to the homogeneous differential equation \frac {d^2y}{dx^2} - 9 /frac {dy}{dx} + 18y = 0.
- (a) Find a particular solution to the nonhomogeneous differential equation y ?? + 4 y ? + 5 y = ? 5 x + 5 e ? x . (b) Find the most general solution to the associated homogeneous differential equati
- Find the general solution to the differential equation y''-2y'-3y=-3te^{-t}
- Find the solution of the homogeneous part of the differential equation given by: y^4 - 2 y '''+ y'' = e^x + e^x \: cos(x) + 2x.
- Find the general solution to the homogeneous differential equation; {d^2}y} \over {d{t^2} - 18dy} \over {dt + 130y = 0
- Show that the following differential equation is homogeneous and then find its solution x(x + y) dy/dx = y (x -y)
- Find the general solution to the following differential equation: xy' + x = y cos (1/x)
- Find the general solution of the differential equation y' + 2y = 4cos 2x; y(pi/4) = 3
- Find the general solution of the differential equation y' = (3xy)(1-\ln y)
- Find the general solution of the differential equation x^2\frac{dy}{dx} = \sqrt y (3x+1)
- Find the general solution of the differential equation. y'' + y' + 3y = 0
- Find the general solution of the differential equation 5y^{(4)} + 3y^{(3)} = 0
- Find the general solution of the differential equation x^2y' + 2 x y = y^3.
- Find the general solution of the differential equation \frac{dy}{dx}+ \frac{y}{x}=-57x+2
- Find the general solution of the differential equation x^2 y'' - 3xy' + 4y =0
- Find the general solution of the differential equation y' = e^{5x} - 9x. y =
- Find the general solution for the differential equation \frac{dy}{dx} = 10 e^{-5x} y =
- Find the general solution of the differential equation y''+y = 3\sin 2t + t\cos 2t
- Find the general solution of the differential equation y' - 5 y = t e^{2 t}.
- Find the general solution to the differential equation \frac{dy}{dt} = \frac{1}{t}y + t^4
- Find the general solution of the differential equation. dy/dx = x - 16/x, (-1, 0)
- Find the general solution of the differential equation y^2dy + x^2dx=0
Explore our homework questions and answers library
Browse
by subject