Question

Solve y'=(y^3+2xy^2+x^2*y+x^3)/(x(y+x)^2) implicitly.

Answer 1

I got (u+1)^2 du=dx/x
integrate,
(u+1)^3/3=ln abs(x)+C
(u+1)^3=3ln abs(x)+C
u+1=(3*ln abs(x)+C)^1/3
u=(3*ln abs(x)+C)^(1/3)-1
y/x=(3*ln abs(x)+C)^(1/3)-1
But the answer in the book is (y+x)^3=3x^3(ln abs(x)+C). How do I get to the answer from there?

Answer 2

@myininaya

Answer 3

this looks same as previous problem ?

Answer 4

Yes, but how do I get to the answer from there? The answer I got is different from the answer in the book. It's a bit strange.

Answer 5

(u+1)^3=3ln abs(x)+C

substitute u = y/x

Answer 6

so I substitute that now? I substituted after I solved for u.

Answer 7

you don't need to solve u or x or y explicitly unless you're asked explicitly to solve in the question