# Thread: general solution of differential equation (express y in term of x)

1. ## general solution of differential equation (express y in term of x)

i got stucked here. below is the answer given. can anybody help please?

2. ## Re: general solution of differential equation (express y in term of x)

I have no idea what you are trying to do here!

First, I would write the equation as $\frac{dy}{dx}+ 2\frac{y}{x}= 2 tan^{-1}(x)$
This is a linear equation so there is a standard formula for the "integrating factor", a function, v(x), so that multiplying by it will make the left side an "exact derivative": $v(\frac{dy}{dx}+ 2\frac{y}{x})= v\frac{dy}{dx}+ 2v\frac{y}{x}= \frac{dvy}{dx}= 2tan^{-1}(x)$.

This leads to an integral that looks difficult if not impossible to integrate with elementary functions so you may have to write the function with an indicated integration.

3. ## Re: general solution of differential equation (express y in term of x)

i redo the question but how to integrate arc tan x ?