Show that `y=a cos(log x)+b sin(log x)` is a solution of the differential equation `x^2(d^2y)/(dx^2)+x(dy)/(dx)+y=0`

Show that y=a cos(log x)+b sin(log x) is a solution of the differential equation x^(2)(d^(2)y)/(dx^(2))+(dy)/(dx)+y=0

y = log x + c is a solution of the differential equation x(d^(2)y)/(dx^(2)) + (dy)/(dx) = 0

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

Verify that y=log x+c is a solution of the differential equation x d^2y/dx^2+dy/dx=0

Show that y=sin (sin x) is a solution of differential equation (d^2y)/(dx^2)+(tan x)(dy)/(dx) +y cos^2 x=0

The solution of the differential equation x log x(dy)/(dx)+y=2log x is

Verify that x^(2)=2y^(2)log y is a solution of the differential equation (x^(2)+y^(2))(dy)/(dx)-xy=0.

Find the general solution of the differential equation x (dy)/(dx)+2y=x^(2)log x .