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

IF x=(a+bt)e^(-nt) , show that , (d^2x)/(dt^2)+2ndx/dt+n^2x=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=A e^(m x)+B e^(n x) , show that (d^2y)/(dx^2)-(m+n)(dy)/(dx)+m n y=0

If y=A e^(m x)+B e^(n x) , show that (d^2y)/(dx^2)-(m+n)(dy)/(dx)+m n y=0 .

If y=A e^(m x)+B e^(n x) , show that (d^2y)/(dx^2)-(m+n)(dy)/(dx)+m n y=0

If x^(m).y^(n)= (x+ y)^(m+n) then show that, (d^(2)y)/(dx^(2))=0

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

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

The equation of a simple harmonic motion of a particle is (d^(2)x)/(dt^(2)) + 0.2 (dx)/(dt) + 36x = 0 . Its time period is approximately