Simple differential equation

  • #1
S[e^x]=f(u)^n
23
0

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
 

Answers and Replies

  • #2
sutupidmath
1,631
4
S[e^x]=f(u)^n;1635559 said:

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 [tex]tan(x)=y[/tex] then [tex]arctan(y)=x[/tex] does this help u? Tan and arctan are inverse functions so, tan(arctan x)=x
 
Last edited:
  • #3
S[e^x]=f(u)^n
23
0
but that x only valid under certain bounds right? and I'm having trouble figuring out what those are
 

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