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

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

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

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