Verify that `y=e^(m cos^-1 x)` satisfies the differential equation `(1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)-m^2y=0`

Verify that y=e^(m cos^(-1)x) satisfies the differential equation (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-m^(2)y=0

Verify that y=e^(m sin^(-1)x) is a solution of the differential equation (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-m^(2)y=0.

The order of the differential equation 2x^2(d^2y)/(dx^2)-3(dy)/(dx)+y=0 is

Verify tht y=e^(x) cos bx is a solution of the differential equation (d^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0.

Verify that y=A cos x+sin x satisfies the differential equation cos x(dy)/(dx)+(sin x)y=1

If y=((1)/(2))^(n-1)cos(n cos^(-1)x), then prove that y satisfies the differential equation (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)+n^(2)y=0

Verify that y=e^x(acosx+csinx) is a solution of the differential equation (d^2y)/dx^2-2(dy)/(dx)+2y=0

Verify that y=log(x+sqrt(x^(2)+a^(2))) satisfies the differential equation d^(2)(y)/(dx^(2))+x(dy)/(dx)=0

Show that y=be^(x)+ce^(2x) is a solution of the differential equation (d^(2)y)/(dx^(2))-3(dy)/(dx)+2y=0