## anonymous 2 years ago 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.

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1. UnkleRhaukus

do you have a solution ?

2. anonymous

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...

3. UnkleRhaukus

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