Simple Separable Differential Equation

[BarackObama]

Homework Statement

y' = y^2sinx

Homework Equations

The Attempt at a Solution

dy/dx = y^2sinx
dy/y^2 = dxsinx
integral(dy/y^2) = integral(sinxdx)

Aside:
let u = y^2
du = 2ydy
dy = du/2y

ln(abs(y^2))/2y = -cosx+C

integral(du/2y^3) = integral(sinxdx)

 

[tiny-tim]

Good morning, Mr President!

Aside:
let u = y^2
du = 2ydy
dy = du/2y

ln(abs(y^2))/2y = -cosx+C

integral(du/2y^3) = integral(sinxdx)

hmm … you're not going to get a second term like that.

You need the integral of 1/y² …

surely you know what that is anyway?? ​

 

[BarackObama]

Thanks!

y= 1/(cosx + C)

 

[tiny-tim]

Yup!