(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Verify that the following ODE can be reduced to an ODE of separable variables.

[tex]\frac{dy}{dx} =f(ax+by+c)[/tex] where a, b and c are constants.

2. The attempt at a solution

I think I must show that there exist functions g and h such that [tex]g(y)dy=h(x)dx[/tex].

I have that [tex]dy=f(ax+by+c) dx[/tex]. I was at a loss. So I talked to a friend and he told me to write [tex]u=ax+by+c[/tex].

So I get [tex]dy=f(u)dx \Rightarrow y= \int f(u)dx=\frac{u-ax-c}{b}[/tex], [tex]y'=\frac{u'-a}{b}[/tex], [tex]y''=u''[/tex]. I want to write [tex]f(u)[/tex] as [tex]\phi _1 (x) \phi _2 (y)[/tex] but I'm totally stuck.

I'd love a tip.

Thank you.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: ODE, seperation of variable

**Physics Forums | Science Articles, Homework Help, Discussion**