(Differential Equations)
Find the general solution of
(sin2 x)y′′ − (2sinxcosx)y′ + (cos2 x + 1)y = sin3 x
given that y1 = sin x is a solution of the corresponding homogeneous equa- tion.
Hint: Use the method of reduction of order to find a second linearly inde- pendent solution y2 to the corresponding homogeneous equation. Then apply the method of variation of parameters to find a particular solution to non- homogeneous equation.
