The solution of differential equation ` cos x dy = y (sin x - y ) dx, 0 lt x lt pi //2 ` isA. `sec x = (tan x + C)y`B. `y sec x = tan x +C`C. ` y tan x = sec x +C`D. ` tan x = (sec x + C)y`

The solution of differential equation ` cos x dy = y (sin x - y ) dx,

1.	The solution of differential equation ` cos x dy = y (sin x - y ) dx, 0 lt x lt pi //2 ` isA. `sec x = (tan x + C)y`B. `y sec x = tan x +C`C. ` y tan x = sec x +C`D. ` tan x = (sec x + C)y`
Answer» Correct Answer - a Since , ` cos x dy = y sinx dx - y^(2)dx` ` rArr 1/(y^(2))(dy)/(dx) -1/y = (dz)/(dx)` ` rArr (dz)/(dx) +(tanx) z = - sec x` This is a linear differential equuation . Therefore `IF = e^(int tanx dx) = e^(log(secx)) = sec x` Hence, the solution is ` z* (sec x) = int - sec x * sec x dx +C_(1)` ` rArr-1/y secx = - tan x + C_(1)` ` rArr sec x = y(tan x +C) " " [ C = -C_(1)]`

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The solution of differential equation ` cos x dy = y (sin x - y ) dx, 0 lt x lt pi //2 ` isA. `sec x = (tan x + C)y`B. `y sec x = tan x +C`C. ` y tan x = sec x +C`D. ` tan x = (sec x + C)y`

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