On page 52 of Differential equations by Zill there is a question to find an explicit solution of the given initial-value problem.
$$\text{30. }\frac{dy}{dx} = y^2 \sin(x^2) ,\qquad y(-2) = \frac{1}{3}$$
so I seperated the $y$'s from the $x$'s and took the integral of the $y$ side but can't figure out the $\sin(x^2)$ integral
$$\frac{-1}{y} + C = \int \sin(x^2)dx $$
Anyone know how to do that?
$$y = \frac{1}{3-\int_{-2}^x \sin(u^2) \, du}$$
Presumably, the point is that you should still solve for $y$ given the boundary condition, even though the integral cannot be evaluated in terms of elementary functions.