Chapter 6 - Differential Equations - 6.1 Exercises - Page 404: 51

$y=\frac{1}{2}e^{x^2} +C$

Begin by using separation of variables then integrating. $\frac{dy}{dx}= xe^{x^2}$ $\int dy = \int xe^{x^2}dx $ Use u substitution, making $u=x^2$ $y= \frac{1}{2}\int e^u du$ $y= \frac{1}{2} e^{x^2} +C$