Find the general solution of xdy + (3xy + y - e^(-3x)) * dx = 0

Zack Chase 2022-09-22 Answered
Find the general solution of x d y + ( 3 x y + y e 3 x ) d x = 0
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Answers (1)

Matthias Calhoun
Answered 2022-09-23 Author has 11 answers
Find the general solution of
x d y + ( 3 x y + y e 3 x ) d x = 0
we have a differential equation as
( 3 x y + y e 3 x ) d x + x d y = 0 (i)
M y = 3 x + 1 , N x = 1
Now, M y N x N = 3
I f = e 3 d x = e 3 x
Multiply by e 3 x  to  E q n (i)
( 3 x y e 3 x + e 3 x y 1 ) d x + x e 3 x d y = 0
Solution: ( 3 x y e 3 x + e 3 x y 1 ) d x + N d y = C y 3 x e 3 x d x + y e 3 x 3 x + 0 = c y x e 3 x 3 e 3 x 3 d x + y e 3 x 3 x = c x y e 3 x e 3 x y 3 + e 3 x y 3 x = c x y e 3 x x = c
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