Question

find the general solution of the differential equation, xy'+y=1+x.

Answer 1

Can you find the solution to the homogeneous version?

Answer 2

If i can find any I wouldn't ask

Answer 3

Good luck then.

Answer 4

laughing out loud

Answer 5

use d(xy) =xdy+ydx

Answer 6

but x is separate, it's like x·y'+y=1+x

Answer 7

xy'+y=1+x can be stated as
xdy/dx +y = 1+x ==>> xdy +ydx =(1+x)dx
d(xy) = (1+x)dx

Answer 8

now integrate both sides..
we have
xy = x+x^2 /2 +c

Answer 9

oh i got it thx!!

Answer 10

welcome dear....