Question

Use separation of variables to solve the differential equation dy/dx = (1+x)/xy with initial condition y(1)=-2.

Answer 1

1/2 y^2 = ln lxl +x + 1
1/2 y^2 = 1/2(x+1)^2
1/2 y^2 = (x+1)^2 +3
1/2 y^2 = ln lxl +x -3
This one can be separated, but it's impossible to solve using techniques of antidifferentiation.

Answer 2

@freckles

Answer 3

@zimmah

Answer 4

I believe it is either the first one or the fourth one.

Answer 5

Actually I figured it out, it is the first one.

Answer 6

let me help

Answer 7

I found out the answer. It's the first one.

Answer 8

wait lets prove it

Answer 9

dy/dx = (1+x)/xy you were told to solve

Answer 10

\[ dy/dx = (1+x)/xy \]

Answer 11

first try to seprate all x to one side and all y to the other

Answer 12

\[ydy=(1+x)dx/x \]

Answer 13

now intigrate

Answer 14

\[\int\limits_{}^{}ydy=\int\limits_{}^{}(1+x)/x dx\]

Answer 15

but recall that

Answer 16

\[(1+x)/x=1/x+x/x \]

Answer 17

\[y^2/2=lnx+x +c\]

Answer 18

guess u don't need help