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 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.

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

Verify that y=c e^(t a n-1_x) is a solution of differential equation (1+x^2)(d^2y)/(dx^2)+(2x-1)(dy)/(dx)=0.

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

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

If sqrt(y)=cos^(-1)x , then it satisfies the differential equation (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)=c , where c is equal to-

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

Verify that the function y=e^(-3x) is a solution of the differential equation (d^2y)/(dx^2)+(dy)/(dx)-6y=0

Verify that the function y=e^(-3x) is a solution of the differential equation (d^2y)/(dx^2)+(dy)/(dx)-6y=0