The question asks me to solve the following equation.

3(x^2 + y^2)dx+x(x^2 + 3y^2 + 6y)dy = 0

I verified that this form is not exact by differentiating M with respect to y and N with respect to x and saw they were not equal. the problem now is to find a suitable u(x,y) such that when I multiply it by the equation, the equation becomes exact.

one of the ways I tried to transform the equation was to see if it was linear. what I got was

x' - x (3y^2 + 6y)/(x^2+y^2) = -x^3 / (x^2 + y^2) ...

hints would be greatly appreciated. also any good site on typing with Latex. all I get are 'unknown errors'