This equation is separable, but [tex]\sin(x^2)[/tex] doesn't have an elementary antiderivative. However, we can use the fundamental theorem of calculus to find a solution in terms of an integral:
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\sin(x^2)[/tex]
[tex]\implies y(x)=y(\sqrt\pi)+\displaystyle\int_{\sqrt\pi}^x\sin(u^2)\,\mathrm du[/tex]
[tex]\implies y(x)=4+\displaystyle\int_{\sqrt\pi}^x\sin(u^2)\,\mathrm du[/tex]
