Copyright

Find a function f such that f(3) = 2 and (t^2 + 1)f^{\prime}(t) + (f(t))^2 + 1 = 0 for t not...

Question:

Find a function f such that f(3) = 2 and {eq}(t^2 + 1)f^{\prime}(t) + \left[f(t)\right]^2 + 1 = 0 {/eq} for {eq}t \neq 1 {/eq}.

Separable Differential equations:

This problem involves solving a given separable differential equation. A differential equation is said to be separable, we can isolate the variables to either side of the equation. For example, let's say we have an ODE as -

{eq}\displaystyle \frac{dy}{dx} = g(y) \times f(x) {/eq}

Then, we can separate the variables as -

{eq}\displaystyle \frac{dy}{g(y)} = f(x) dx {/eq}

Answer and Explanation: 1

Become a Study.com member to unlock this answer!

View this answer

Given a function {eq}\displaystyle f(x) {/eq} such that,

{eq}\displaystyle f(3) = 2 {/eq}

And,

{eq}\displaystyle (t^2+1) f'(t) + ((f(t))^2 +...

See full answer below.


Learn more about this topic:

Loading...
Separable Differential Equation: Definition & Examples

from

Chapter 16 / Lesson 1
6.2K

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

Explore our homework questions and answers library