IF `x=(a+bt)e^(-nt)`, show that , `(d^2x)/(dt^2)+2ndx/dt+n^2x=0`.

Q.if x=(a+bt)e^(-nt), show that,((d^(2)x)/(dt^(2)))+2n((dx)/(dt))+n^(2)=0

If x=Ae^(-(kt)/2)cos(pt+in) , and A,k,p, in are constants, show that (d^2x)/(dt^2)+kdx/dt+n^2x=0 , where n^2=p^2+1/4k^2 .

If y=Acosnt+Bsin nt(A,B,n are constants), show that (d^2x)/(dx^2)+n^2x=0 .

If x=a cos nt-b sin nt , then (d^2x)/(dt^2)=

If x^2=t^2+! then find (d^2x)/(dt^2)

If x=a cos nt-b sin nt, then (d^(2)x)/(dt^(2)) is n^(2)x( b) -n^(2)x( c) nx( d )nx

If x=a cos nt-b sin nt, then (d^(2)x)/(dt^(2)) is n^(2)x(b)-n^(2)x(c)-nx(d)nx

If the solution of the equation (d^(2)x)/(dt^(2))+4(dx)/(dt)+3x = 0 given that for t = 0, x = 0 and (dx)/(dt) = 12 is in the form x = Ae^(-3t) + Be^(-t) , then

If the solution of the equation (d^(2)x)/(dt^(2))+4(dx)/(dt)+3x = 0 given that for t = 0, x = 0 and (dx)/(dt) = 12 is in the form x = Ae^(-3t) + Be^(-t) , then

If the solution of the equation (d^(2)x)/(dt^(2))+4(dx)/(dt)+3x = 0 given that for t = 0, x = 0 and (dx)/(dt) = 12 is in the form x = Ae^(-3t) + Be^(-t) , then