`x=(a+b t)e^(-n t),p r o v e t h a t(d^2x)/(dt^2)+2n(dx)/(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 = a ( cos t + t sint) and y = a (sin t - t cost), 0 < t < pi/2 , find (d^2x)/(dt^2),(d^2y)/(dt^2)

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

If x=f(t )cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost ,t h e n((dx)/(dt))^2+((dy)/(dt))^2

If x= f(t )cost-f^(prime)(t)sinta n dy=f(t)sint+f^(prime)(t)cost ,t h e n((dx)/(dt))^2+((dy)/(dt))^2 (a) f(t)-f^(primeprime)(t) (b) {f(t)-f^(primeprime)(t)}^2 (c) {f(t)+f^(primeprime)(t)}^2 (d) none of these

If t a n y=(2^x)/(1+2^(2x+1)),t h e n(dy)/(dx) at x=0 is

If t a n y=(2^x)/(1+2^(2x+1)),t h e n(dy)/(dx) at x=0 is