Can somebody check this:
solve differential equation y'y'''=2(y'')^2 if know that it's derivative of lower-ordered differential equation.

I'll write my solution.

Question

Can somebody check this:
solve differential equation y'y'''=2(y'')^2 if know that it's derivative of lower-ordered differential equation.

I'll write my solution.

nikvist · Answer

nikvist · Answer

Try, $$y'y'''=2(y'')^2\quad,\quad z=y'$$$$zz''=2(z')^2$$$$\frac{z''}{z'}=2\frac{z'}{z}$$$$(\ln{z'})'=2(\ln{z})'\quad\dots$$

gg · Answer

I did it in different way than wolfram did, but I didn't get the same result. I found a mistake :)