If `y= a cos (log x)+b sin (log x)`, show that `x^(2) (d^(2)y)/(dx^2)+x(dy)/(dx)+y=0`.

If y=Acos(logx)+B sin(logx) then prove that x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx)+y=0 .

If y = a sin (log x) + b cos (log x) , then prove that : x^2 d^2y/dx^2+ x dy/dx+ y = 0 .

If y = 3 cos (log x) + 4 sin (log x) show that x^2 y_2 + xy_1 + y = 0

Find the second order derivative of the following functions If y = log[x + sqrt(x^2 + a^2)] , show that (x^2 + a^2) (d^2y)/(dx^2) + x (dy)/(dx) = 0

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

IF y =[log (x+ sqrt(1+ x^2))]^2 ,show that (1+ x^2) (d^2y) /dx^2 +x(dy/dx) =0

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

If x = a cos θ + b sin θ and y = a sin θ − b cos θ , then prove that y^2(d^2y)/(dx^2)-x(dy)/(dx) +y=0