Solve the initial value problem.

$y^{\text{'}}=xsin(x^2),y(\sqrt[\phantom{2}]{\frac{}{2}})=1$

$y=-\frac{1}{2}cos(x^2)+1$

The question has already been solved with the correct answer. I need it solved with phthon solver. Please provide screenshots of both the code used from chatgpt and the output in python solver with the correct answer