Question

How to separate the variables and find the integral of dy/dx=y^2/x^3

Answer 1

This is what I have so far:
\[x^3dy=y^2dx\]
\[\int\limits(dy/y^2)=\int\limits(dx/x^3)\]

Answer 2

\[\int\limits y ^{-2}dy=\int\limits x ^{-3}dx+c\]
solve

Answer 3

how did you get that? please show step by step

Answer 4

\[\frac{ 1 }{ x ^{m} }=1*x ^{-m}\]
it is the next step to what you have written.

Answer 5

oh! ok. so if i do the integral i'll get \[\frac{ 1 }{ y }=-\frac{ 1 }{ 2} x ^{-2 } +C\]
is that correct?

Answer 6

sorry, \[-\frac{ 1 }{ y }\]

Answer 7

correct

Answer 8

Thank you!