Prove that , ` x = A cos sqrt(mu t)` is a solution of the differential equation
` (d^(2)x)/(dt^(2)) + mu x = 0`

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

Show that the function y= A cos 2x - B sin 2x is a solution of the differential equation (d^(2)y)/(dx^(2)) + 4y = 0

Find the general solution of the differential equation x (dy)/(dx) + 2y = x^(2)(x ne 0) .

Find the general solution of the differential equation (dy)/(dx) + sqrt((1 - y^(2))/(1 - x^(2))) = 0 .

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

The solution of the differential equation {1+xsqrt((x^2+y^2))}dx+{sqrt((x^2+y^2))-1}ydy=0 is equal to

Show that , the solution x = A cos (nt + B) + (k)/(n^(2) - p^(2)) . Sin pt , for all A and B satisfies the differential equation (d^(2) x)/(dt^(2)) + n^(2)x = k sin pt .

If u(x) and v(x) are two independent solutions of the differential equation (d^(2)y)/(dx^(2))+b(dy)/(dx)+cy=0 , then additional solution (s) of the given differential equation is (are)

If u(x) and v(x) are two independent solutions of the differential equation (d^(2)y)/(dx^(2))+b(dy)/(dx)+cy=0 , then additional solution(s) of the given differential equation is (are)-

Show that , the solution x = e^(-kt) (a cos nt + b sin nt ), for all a and b , always satisfies the differenital equation (d^(2)x)/(dt^(2)) + 2k (dx)/(dt) + (k^(2) + n^(2)) x = 0