integrating factor

**poorna** · May 1st 2010, 09:42 AM

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

**Krizalid** · May 1st 2010, 10:00 AM

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

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