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.

Answer 1

http://www.wolframalpha.com/input/?i=y%27y%27%27%27%3D2%28y%27%27%29%5E2

Answer 2

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

Answer 3

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