Solve by reduction of order:
yy''=3y'^2

The answer the book has is y=(c1*x+c2)^(-1/2)
I can't figure out how to put it in standard form to get the above answer.

Question

Solve by reduction of order:
yy''=3y'^2



The answer the book has is y=(c1*x+c2)^(-1/2)
I can't figure out how to put it in standard form to get the above answer.

unklerhaukus · Answer

do you have a solution ?

anonymous · Answer

No, I'm not sure how to go about doing this problem :/
I know that for a homogeneous 2nd order ODE, the solution is y=c1y1+c2y2
but since the above equation cannot be put in standard form I can't see how to solve it.

I should add that the problem wants me to use reduction of order, where I first pick a y1 solution by inspection, then get y2 using: $$y_2=y_1u=y_1\int\limits_{}^{}U\;dx$$
where $$U=\frac{ 1 }{ y^2 }e^{-\int\limits_{}^{}p\;dx}$$
I can do it for a regular problem but I'm lost on this one...

unklerhaukus · Answer

so first we need to find $y_1$, a solution to the equation, i'm not sure how to do this