Solve the Equation: (dy)/(dx)-y tan x=e^(-2x)

Yair Valentine

Yair Valentine

Answered question

2022-08-03

Solve the Equation:
d y d x y tan x = e 2 x

Answer & Explanation

Barbara Klein

Barbara Klein

Beginner2022-08-04Added 19 answers

Given equation is:
d y d x y tan x = e 2 x ...(1)
This is a linear equation of first order in y
where P = tan x   a n d   Q = e 2 x
P d x = tan x d x = log | sec x | = log | ( sec x ) 1 | = log | cos x |
Integrating Factor = e P d x = e log | cos x | = cos x
Now the general solution of the given equation is
y e P d x = Q e P d x d x
y cos x = e 2 x cos x d x
y cos x = e 2 x 4 + 1 ( 2 cos x + sin x )
y cos x = e 2 t 5 ( sin x 2 cos x ) + C

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