Question

sinxdy + ycosxdx = 4xdx
$\Rightarrow$ d(y.sinx) = 4xdx
Integrate we get
$\Rightarrow$ y.sinx = 2x² + C
$\Rightarrow$passes through $\left(\frac{\pi }{2}, 0\right)\Rightarrow 0=\frac{{\pi }^2}{2}+C$
$\Rightarrow$ C = - $\frac{{\pi }^2}{2}$
$\Rightarrow$ysinx = 2x² - $\frac{{\pi }^2}{2}$is the solution
$y\left(\frac{\mathrm{\pi }}{6}\right)=\left(2.\frac{{\mathrm{\pi }}^2}{36}-\frac{{\pi }^2}{2}\right)2=-\frac{8{\pi }^2}{9}$