If `y=1/(2)^(n-1)cos(ncos^(-1)x),` then prove that `y` satisfies the differential equation `(1-x^2)` `(d^2y)/(dx^2)-x(dy)/(dx)+n^2y=0`

Similar Questions

Explore conceptually related problems

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

Solve the differential equations. (dy)/(dx)=(x^(2))/(1+y^(2))

(1+x^(2))(dy)/(dx) = 1-y

Solve the differential equation x y(dy)/( dx)=(1+y^2)/(1+x^2)(1+x+x^2)

The solution of the differential equation x(x^2+1)((dy)/(dx))=y(1-x^2)+x^3logx is

The solution of the differential equation (x^2y^2-1)dy+2xy^3dx=0 is

The order of the differential equation ((d^(2)y)/(dx^(2)))^(3)=(1+(dy)/(dx))^(1/2) is

Solution of the differential equation {1/x-(y^2)/((x-y)^2)}dx+{(x^2)/((x-y)^2)-1/y}dy=0 is

Solve the following differential equation: sqrt(1+x^2+y^2+x^2\ y^2)\ +x y(dy)/(dx)=0

Show that y=e^(-x)+mx+n is a solution of the differential equation e^(x)(d^(2)y)/(dx^(2))-1=0.