Find ∫x2sin2x dx\int x^2 \sin 2x \, dx∫x2sin2xdx
Hence solve the differential equation
dydt=(tsinty)2 \frac{dy}{dt} = \left(\frac{t \sin t}{y}\right)^2 dtdy=(ytsint)2giving your answer in the form yn=f(t)y^n = f(t)yn=f(t) where nnn is an integer.
