I am trying to solve non exact differential equation but I am unable to find the integration factor.
I solve the following question
$$-3y\frac{dy}{dx}+2x=0 $$
and I get the integrationg factor $x^{-5/2}$ and I use the proper way to find the integrating factor, but in our text book the integrating facot for above differential equation is finded and that is $y/x^4$.
Now I am completely confused that why please help me out with this.
Best Answer
$$-3y\:dy+2x\:dx=0$$ is an EXACT differential equation.
In other words the integrating factor is $1$. $$d\left(-\frac32 y^2+x^2\right)=0$$ $$-\frac32 y^2+x^2=\text{constant}$$