Question

Help with nonlinear differenctial equations method

We learn this method about parameters where we put p=dy/dx=y'=xt , I have no idea what it is called but if anyone knows about or where i can read about it please tell me

Answer 1

Here is an example that we got \[if x=\phi(x)\]\[y=\int\limits_{?}^{?}p \frac{ d \phi(p) }{ dp }dp+c\]

Answer 2

or x=p+sin(p/x) where p=y' , WHERE DO THEY GET THIS FROM I DONT UNDERSTAND
then \[x=\frac{ sint }{ 1-t }\]
\[p=\frac{ t \sin(t) }{ 1-t }\]
\[dy=t \sin(t)*\left[\frac{ (1-t)cost+sint }{ 1-t^3 } \right]dt\]

Answer 3

on the example above p=y'=xt WHY?