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

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

If x= A cos 4t + B sin 4t , then (d^(2)x)/(dt^(2))=

If x=a cos nt-b sin nt and (d^(2)x)/(dt^(2))=lambda x then find the value of lambda.

If x=A cos 4t+B sin4t, then (d^(2)x)/(dt^(2)) is equal to

If x=A cos 4t+B sin4t, then (d^(2)x)/(dt^(2)) is equal to

If y=(1)/(sqrt(a^(2)-b^(2)))cos^(-1)((a cos x+b)/(a+b cos x)), then (d^(2)y)/(dx^(2))=(i)(b sin x)/((a+b cos x)^(2))( ii) -(b sin x)/((a+b cos x)^(2))( iii) (b cos x)/((a+b cos x)^(2))( iii) -(b cos x)/((a+b cos x)^(2))

If y=a sin 2x+b cos 2x satisfies the equation (d^(2)y)/(dx^(2))=6 sin 2x-cos2x, then (a, b)-=

dx/dt + x cos t = 1/2 sin 2 t

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