Question

Solve y'=(2y^2+(x^2)(e^(-(y/x)^2)))/(2xy) explicitly.

Answer 1

y=ux
u=y/x
y'=u+u'x
y'=y/x+(xe^(-(y/x)^2))/2y
u'x+u=u+x/(2ye^(u^2))
u'x=(1/2)(1/u)(1/e^(u^2))
u'x=1/(2ue^(u^2))
2ue^(u^2) du=dx/x
t=u^2
dt=2u du
e^t dt=dx/x
e^t=ln abs(x)+C
e^(u^2)=ln abs(x)+C
u^2=ln(ln abs(x)+C)
u=+/-sqrt(ln(ln abs(x)+C))
y=+/-x*sqrt(ln(ln abs(x)+C))
But the answer in the book says y=+/-x*ln(ln abs(x)+C). So which answer is right? My answer or the answer in the book?

Answer 2

@hartnn

Answer 3

is this even possible to answer?

Answer 4

What do you mean?

Answer 5

its certainly complex!!

Answer 6

You know what, it'd be good if the user sithsandgiggles is here.

Answer 7

I don't see any error in your work.

Answer 8

So the answer in the book must be wrong, then. Right?

Answer 9

There could be multiple *equivalent* answers for the same question, but i don't see any way for those 2 answers to be equivalent.
So yes, we can safely conclude that the answer in the book is incorrect.

Answer 10

Thank you!

Answer 11

theres certainly got to be a sqrt in the answer