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The general solution of differential equ...

The general solution of differential equation `(dy)/(dx)=e^((x^(2))/(2))+xy` is

A

`y=Ce^(-x^(2)//2)`

B

`y=Ce^(x^(2)//2)`

C

`y=(x+C)e^(x^(2)//2)`

D

`y=(C-x)e^(x^(2)//2)`

Text Solution

AI Generated Solution

To solve the differential equation \(\frac{dy}{dx} = e^{\frac{x^2}{2}} + xy\), we will follow these steps: ### Step 1: Rearranging the Equation We start by rearranging the equation to isolate the terms involving \(y\): \[ \frac{dy}{dx} - xy = e^{\frac{x^2}{2}} \] ...
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