If `y=e^(-x)cosxa n dy_n+k_n y=0,w h e r ey_n=(d^n y)/(dx^n)a n dk_n` are constants `AAn in N ,` then (a)`k_4=4` (b) `k_8=-16` (c)`k_(12)=20` (d) `k_(16)=-24`

If y=e^(-x)cos x and y_(n)+k_(n)y=0 where yn=(d^(n)y)/(dx^(n)) and k_(n) are constant n in N then

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^r=(n !^(n+r-1)C_(r-1))/(r^n),w h e r en=k r(k is contstant), then ("lim")_(rvecoo)y is equal to (a)(k-1)(log)_e(1+k)-k (b)(k+1)(log)_e(1-k)+k (c)(k+1)(log)_e(1-k)-k (d)(k-1)(log)_e(1-k)+k

If y=ax^(n+1)+bx^(-n), then x^(2)(d^(2)y)/(dx^(2))=n(n-1)y(b)n(n+1)y(c)ny(d)n^(2)y

If m,n,k are rational and m=K+(n)/(K) then the roots of x^(2)+mx+n=0 are

If 4th term in the expansion of (kx+ 1/x)^n is 5/2 then (A) n=8 (B) n=6 (C) k=1/4 (D) k=1/2

x^(n)+y^(n) is divisible by (x+y) is true when n(in N) is of the form (k in N) .