
integrating factor
Hello
The integrating actor of the diferential eqn
2cos(y^2)dx  xysin(y^2) dy = 0 is
a) e^x
b) e^(x)
c) 3x
d) x^3
Writing in terms of dx/dy I got the anwer to be (cos(y^2))^(1/4). its not even one of the options
But in terms of dy/dx I dont know what the answer is :(

Suppose we want to find an integrating factor only dependent of $\displaystyle x,$ then let $\displaystyle M(x,y)=2\cos y^2$ and $\displaystyle N(x,y)=xy\sin y^2$ and see that $\displaystyle \frac1N\left(\frac{\partial M}{\partial y}\frac{\partial N}{\partial x}\right)=\frac3x,$ thus $\displaystyle u(x)=\exp\left(\int\frac3x\,dx\right)=x^3$ is the integrating factor we want.