If y = ax sin x show that
`x^2y_2 - 2xy_1 + (x^2 + 2)y = 0`

If y=e^(ax)sinbx show that y_2-2ay_1+(a^2+b^2)y=0 .

If y =(sin^(-1) x)^2 , prove that (1-x^2)y_2 - xy_1 - 2 = 0

If y = tan^(-1) x, prove that (1 + x^2)y_2 + 2xy_1 = 0

If y= tan^-1 x then prove that (1+x^2) y_(2) + 2xy_(1) =0. Differentiate sec^-1(1/(2x^2 -1)) with respect to sqrt 1-x^2 .

If y = e^(m cos^(-1) x) (1-x^2)y_2-xy_1 = m^2y

If y=3cos(logx)+4sin(logx) , then show that x^(2)y_(2)+xy_(1)+y=0 .

If y = sin(mcos^(-1)x) then prove that (1-x^(2))y_(2)-xy_(1)+m^(2)y=0 .

If y=(tan^(-1)x)^2 then show that (x^2+1)^2 (d^2y)/(dx^2)+2x(x^2+1)((dy)/(dx))=2 .

If y=sin^(-1) x, then show that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)=0