Suppose {eq}\frac{\mathrm{d}y}{\mathrm{d}t} + y = e^{-t} {/eq} and {eq}y(0) = 2 {/eq}. Find {eq}y(t) {/eq}.
Question:
Suppose {eq}\frac{\mathrm{d}y}{\mathrm{d}t} + y = e^{-t} {/eq} and {eq}y(0) = 2 {/eq}. Find {eq}y(t) {/eq}.
First Order Linear Differential Equation
A first order linear differential equation is an equation expressed in the form {eq}\dfrac{\mathrm{d}y}{\mathrm{d}t} + P(t)\,y = Q(t) {/eq}. To solve this type of differential equation, determine the integrating factor for the equation using the equation {eq}I = e^{\int P(t) \,\mathrm{d}t} {/eq}.
Answer and Explanation:
Become a Study.com member to unlock this answer! Create your account
View this answerThe given differential equation is a first order linear differential equation in the form {eq}\dfrac{\mathrm{d}y}{\mathrm{d}t} + P(t)\,y =...
See full answer below.
Learn more about this topic:
from
Chapter 16 / Lesson 3Learn to define what a linear differential equation and a first-order linear equation are. Learn how to solve the linear differential equation. See examples.