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

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

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

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

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

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

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