Nonlinear OD transform to linear ODE

[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 don't know where to begin.

Homework Equations

Thank you guys!

 

[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.

 

[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.