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

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

Solution of differential equation (dt)/(dx)=(xlogx)/(t) is

Prove that xy= ae^(x)+be^(-x)+x^(2) is the general solution of the differential equation x(d^(2)y)/(dx^2)+2(dy)/(dx)-xy+x^(2)-2=0

Prove that xy=ae^(x)+be^(-x)+x^(2) is the general solution of the differential equation x(d^(2)y)/(dx^(2))+2(dy)/(dx)-xy+x^(2)-2=0.

If x = x(t) is the solution of the differential equation (t 1)dx = (2x (t 1)^4) dt, x(0) = 2 , then, x(1) equals ___________.

The solution of differential equation (dt)/(dx) = (t[d/dx{g(x)}]-t^(2))/(g(x) ) is

Let x=x(t) and y=y(t) be solutions of the differential equations (dx)/(dt)+ax=0 and (dy)/(dt)+by=0] , respectively, a,b in R .Given that x(0)=2,y(0)=1 and 3y(1)=2x(1) ,the value of "t" ,for which, [x(t)=y(t) ,is :

What is the values of frequency in the differential equation of SHM (d^(2)x)/(dt^(2))+100x =0 ?