Dy/dx = (y^2) /x , form differential equation

[goldfish9776]

Homework Statement

my ans is lnx = (-1/y) + c
(-1/y) = lnx -c
y = -1/ (lnx -c ) , but the answer given is (-1/ln x )+ C , how to get the answer given ?

Homework Equations

The Attempt at a Solution

 

[Qwertywerty]

Your solution seems fine. I believe the given answer may be wrong.

 

[LCKurtz]

You can easily verify that your answer is correct and the given answer is wrong by plugging them back into the original DE. By the way, you should post the original DE in the body, not the title of your post.

The only thing I would change is use $\ln |x|$ in the antiderivative.

 

[Mark44]

Homework Statement

my ans is lnx = (-1/y) + c
(-1/y) = lnx -c
y = -1/ (lnx -c ) , but the answer given is (-1/ln x )+ C , how to get the answer given ?

Homework Equations

The Attempt at a Solution

When you post a question, please put the problem statement into the first section, not the thread title.

Your answer looks fine to me, except that it should be ln|x|, but you should carry it a step further and solve for y. The given answer should have the constant in the denominator, not just added to the fraction as you show it.

 

[epenguin]

And more often than not for a result like that you would be writing, since c is an arbitrary constant

y = -1/(ln x + ln K) where K is another arbitrary constant

= -1/(ln Kx) and thence maybe

x = K' e^-y