Solution verification: $(2x\ln y)\mathrm{d}x+(\frac{x^2}{y}+3y^2)\mathrm{d}y=0$ I've come across this problem while solving an exercise on Exact Differential equations and it's as follows:

Solve the differential equation:
   $$(2x\ln y)\mathrm{d}x+\left(\dfrac{x^2}{y}+3y^2\right)\mathrm{d}y=0$$

So what I've noticed is that if we expand the right side bracket as such:
$$(2x\ln y)\mathrm{d}x+ \dfrac{x^2}{y}\mathrm{d}y+3y^2\mathrm{d}y=0
$$
Is that I can express the first two terms of the above equation as 
$$\mathrm{d}\left(x^2 \ln y\right)$$
Form here, simple integration leads us to:
$$x^2\ln y + y^3= \mathrm{C}$$
Where $\mathrm{C}$ is the constant of integration. The solution on the other hand is given:
$$x^2+\ln y+y^3=\mathrm{C}$$
Is this a misprint or am I missing something somewhere?

$$(2x\ln y)\mathrm{d}x+ \dfrac{x^2}{y}\mathrm{d}y+3y^2\mathrm{d}y=0$$
$$\ln y{d}x^2+{x^2}d \ln y+3y^2\mathrm{d}y=0$$
$$d x^2\ln y+3y^2dy=0$$
Integration gives:
$$x^2\ln y +y^3=C$$
Your answer is perfectly correct.
