Solve the following equation: $P(x,y)+Q(x,y)y^{\text{'}}=(3xy+y^2)+(x^2+xy)y^{\text{'}}=0.$

$($a$)(1$ point$)$ Show that this equation is not exact by comparing $de{l}_{y}P$ and $de{l}_{s}Q.$

$($b$)(1$ point$)$ Find an integrating factor $$ that depends only on $x$ by solving $d\frac{}{d}x=\frac{}{x}.$

$($c$)$ point$)$ Multiply $(x)$ by $(3xy+y^2)+(x^2+xy)y^{\text{'}}=0$ and show the resulting equation is exact.

$($d$)(2$ points$)$ Solve the exact equation from the previous part. Give the solution in implicit form $F(x,y)=c.$ Hint: you should have found $(3x^{2}y+x{y}^2)+(x^3+x^{2}y)y^{\text{'}}=0.$