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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}.

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The given differential equation is a first order linear differential equation in the form {eq}\dfrac{\mathrm{d}y}{\mathrm{d}t} + P(t)\,y =...

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First-Order Linear Differential Equations

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Chapter 16 / Lesson 3
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Learn to define what a linear differential equation and a first-order linear equation are. Learn how to solve the linear differential equation. See examples.


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