Solving a Simple Differential Equation: y' = (x + xy^2)

[S[e^x]=f(u)^n]

Homework Statement

i'm trying to solve the simple differential equation y'=(x+xy^2)


2. The attempt at a solution

i get dy/(1+y^2)=xdx and then integrate over the whole thing getting the solution

arctan(y)=0.5x^2+C

my problem is how do i simply this down to an equation in the form y=...

i must be missing something

 

[sutupidmath]

Homework Statement

i'm trying to solve the simple differential equation y'=(x+xy^2)


2. The attempt at a solution

i get dy/(1+y^2)=xdx and then integrate over the whole thing getting the solution

arctan(y)=0.5x^2+C

my problem is how do i simply this down to an equation in the form y=...

i must be missing something

well remember that if $$tan(x)=y$$ then $$arctan(y)=x$$ does this help u? Tan and arctan are inverse functions so, tan(arctan x)=x

 

[S[e^x]=f(u)^n]

but that x only valid under certain bounds right? and I'm having trouble figuring out what those are