Question

Solve x(ln x)^2*y'=-4(ln x)^2+y*ln x+y^2 explicitly.

Answer 1

The answer I got is...\[y=\frac{ 2lnx(C+(\ln x)^{4^{}}) }{ C-(\ln x)^4 }\]

Answer 2

But the answer in the book is...\[y=\frac{ 2\ln x(1+C(\ln x)^4) }{ 1-C(\ln x)^4 }\]

Answer 3

Which answer is right? My answer or the answer in the book?

Answer 4

@ganeshie8 @iambatman

Answer 5

@ParthKohli @Luigi0210 @zepdrix

Answer 6

They ae the same.
Factor a C out of the numerator AND denominator, cancel them out.

You end up with some new constants 1/c, yes?
Just call those something else, c1 :)

Answer 7

So my answer is correct, right?

Answer 8

If the book answer is correct, then yes yours is also correct :)

Answer 9

Thank you!