Question

(Y+1/y)*2 -5(y+1/y) +4
Is equal to

Answer 1

We have (D2 + 1)y = tanx A.E. is m2 + 1 = 0 i.e., m2 = – 1 i.e., m = ± i C.F. is C.F. = yc = C1cos x + C2sinx ∴ y = A cos x + B sinx ...(1) be the complete solution of the given equation where A and B are to be found We have y1 = cos x and y2 = sin x y′1 = – sinx y′2 = cos x W = y1y'2 - y2y'1 = cos x . cos x + sin x . sin x = cos2x + sin2x = 1 Substitute these values of A and B in Eqn. (1), we get y = {– log(secx + tanx) + sinx + C1} cosx + {– cos x + C2} sinx y=C1cos x + C2sin x – cosx log (sec x + tan x) This is the complete solution.Read more on Sarthaks.com - https://www.sarthaks.com/365315/solve-by-the-method-of-variation-of-parameters-y-y-tanx

Step-by-step explanation: