\begin{document}
\section{Quiz2 TUT0401}
Here is the quiz question and solution
\be
(3x^2y+2xy+y^3) + (x^2+y^2)y' = 0
\ee
Set
\be
M(x,y)=(3x^2y+2xy+y^3) N(x,y)=(x^2+y^2)
\ee
\be
My=3x^2+2x+3y^2 Nx=2x
\ee
Since My is not equal to Nx, therefore, it is not exact
\be
R==(3x^2+2x+3y^2-2x\frac{x^2+y^2}=3
\ee
Thus
\bea
y&=&\sin (\rm ln|x|+C) \quad \text{if} \,\, x\neq0 \text{ and } |y|<1 ; \\
\text{ or } y&=&\pm 1\quad
\eea
\end{document}
