Find the differential equation, if `xy=Ae^(x)+Be^(-x)+x^(2)`

Verify that y=A cos x-B sin x is a solution of the differential equation (d^(2)y)/(dx^(2))+y=0

Write the order and degree of the differential equation x^(2)((d^(2)y)/(dx^(2)))^(1//2)=(dy)/(dx)

Find the order and the degree of the differential equation xy(d^(2)y)/(dx^(2))+x((dy)/(dx))^(2)-y((dy)/(dx))=0