Nonlinear OD transform to linear ODE

1. Oct 6, 2012

guitar24

Hello,

I am confused as to how to transform nonlinear ODEs to linear ones by change of variables. Usually its pretty straight forward and I can do it, but this particular problem has me stumped and I dont know where to begin.

2. Relevant equations

Thank you guys!

2. Oct 6, 2012

HallsofIvy

Where did you see "transforing nonlinear ODEs to linear ones by change of variables"? You can't! Linear and non-linear ODEs have very different qualitative properties which cannot be changed by changing variables. We can approximate non-linear ODEs over varying parts of their range. Perhaps your reference is to changing variable to change the region in which the non-linear ODE can be approximated by a linear equation.

3. Oct 6, 2012

guitar24

Some nonlinear, first order ODEs can be solved. I am supposed to find a change of variables such that the new ODE is variable separable and easily solvable.