Question

If y = x + tan x, show that cos2 x. d2y/dx2 – 2y + 2x = 0

Answer 1

Y= x+tanx
dy/dx=1+ sec2x
d2y/dx2 = 2secx. secxtanx. 2sec2xtanx
d2y/dx2 =2tanx/ cos2x
Cos2x. d2y/dx2 - 2tanx=0
Cos2x.d2y/dx2 - 2x - 2tanx +2x=0
Cos2x.d2y/dx2 - 2y+2x=0

Answer 2

Answer :

Hey Mate,

Given : LHS =>  Y= X + Tan X & RHS = Cos²X × ( d²y/ dx² ) - 2Y + 2X = 0

LHS => Y= X + Tan X

( dy/ dx) = 1 +  Sec²X

(d²y/ dx²) = 2 SecX × SecX TanX × 2Sec²X Tan X

( d²y/ dx² ) = 2 Tan X / Cos²X

Cos² X × ( d²y/ dx² ) - 2 TanX = 0

Cos²X × ( d²y/ dx² ) - 2X - 2 Tan X + 2X = 0

Cos²X × ( d²y/ dx² ) - 2Y + 2X = 0 => RHS

(LHS = Left Hand Side ; RHS = Right Hand Side)