Answer
$y=\pm\sqrt{\ln \left[x^2+2 x^{3 / 2}+c\right]}$
Work Step by Step
$\begin{aligned} & \int 2 y e^{y^2} d y=\int(2 x+3 \sqrt{x}) d x \\ & e^{y^2}=x^2+2 x^{3 / 2}+e^c \\ & \ln e^{y^2}=\ln \left[x^2+2 x^{3 / 2}+c\right] \\ & y^2=\ln \left[x^2+2 x^{3 / 2}+c\right] \\ & \mathrm{y}=\pm\sqrt{\ln \left[x^2+2 x^{3 / 2}+c\right]}\end{aligned}$
