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

Zack Chase

Zack Chase

Answered question

2022-09-22

Find the general solution of x d y + ( 3 x y + y e 3 x ) d x = 0

Answer & Explanation

Matthias Calhoun

Matthias Calhoun

Beginner2022-09-23Added 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

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?