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Find the general solution for the given ODE

{eq}y' = (1 + y^2)e^x {/eq}.

Question:

Find the general solution for the given ODE

{eq}y' = (1 + y^2)e^x {/eq}.

General Solution of Differential Equation:

Given a first order linear differential equation to find the general solution of

this differential equation integrate differential equation with respect to x.

Given differential equation is also first order linear D.E.

So integrate given equation to get value of y.

Use {eq}\displaystyle \int \frac{dx}{x^2+a^2} = tan^{-1} (x/a) {/eq}

Answer and Explanation: 1

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{eq}y' = (1 + y^2)e^x\\ \displaystyle \frac{dy}{dx} = (1 + y^2)e^x\\ \displaystyle \frac{dy}{1+y^2} = e^x dx\\ {/eq}

Integrate above equation

{eq...

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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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