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Vector Algebra

Question
CBSEENMA12036110
Wired Faculty App

Solution of the differential equation
cos x dy = y (sin x - y) dx, 0 < x < π/2, is 

  • sec x = (tan x + C ) y 

  •  y sec x = tan x + C

  •  y tan x = sec x + C 

  •  tan x = (sec x  + C)y

Solution

A.

sec x = (tan x + C ) y 

since cos xdy = y sin x dx - ydx
rightwards double arrow space 1 over straight y squared space dy over dx minus 1 over straight y space tan space straight x space equals space minus space sec space straight x Put space minus 1 over straight y space equals space straight z rightwards double arrow 1 over straight y squared dy over dx space equals space dz over dx rightwards double arrow space dz over dx space plus space left parenthesis tan space straight x right parenthesis straight z space equals space minus space sec space straight x
This is linear differential equation,
Therefore,
IF space equals space straight e to the power of integral tan space straight x space dx end exponent equals space straight e to the power of log space sec space straight x space end exponent space equals space sec space straight x Hence comma space the space solution space is straight z. space left parenthesis sec space straight x right parenthesis space equals space integral negative sec space straight x. space sec space straight x space dx space plus space straight C subscript 1 rightwards double arrow space minus 1 over straight y space sec space straight x space equals space minus space tan space straight x space plus space straight C subscript 1 rightwards double arrow space sec space straight x space equals space straight y space left parenthesis space tan space straight x space plus space straight C right parenthesis

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