Show that the substitution `z=ln(tan(x/2))` changes the equation `(d^2y)/(dx^2)+ cot xdy/(dx) +4ycosec^2x=0` to `(d^2y)/(dx^2)+4y`.

Show that the substitution z=ln(tan((x)/(2))) changes the equation (d^(2)y)/(dx^(2))+cot x(dy)/(dx)+4y cos ec^(2)x=0 to (d^(2)y)/(dx^(2))+4y

If y=cos (sin x) , show that (d^2y)/(dx^2)+tan x""(dy)/(dx)+y cos^2 x=0

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

If y = tan^(-1)x show that (1+x^2)(d^2y)/(dx^2) + 2x(dy)/(dx) = 0

Show that the function y=Ax+B/x is a solution of the differential equation x^2(d^2y)/dx^2+xdy/dx-y=0 .

The order of the differential equation (d^4y)/(dx^4)+((dy)/(dx))^3-y(d^2y)/(dx^2)=0 is

If y=cot x show that (d^(2)y)/(dx^(2))+2y(dy)/(dx)=0

If y=xlog (x/(a+bx)) , prove that x^3(d^2y)/(dx^2)=(y-xdy/dx)^2 .