Solving a first order differential equation

[fred_91]

Homework Statement

Solve the differential equation:
dy/dx = 2/(x+e^y)

Homework Equations

The Attempt at a Solution

I tried to use the substitution v=x+e^y, but I didn't get very far:

v’=1+e^y y’
v’-1=(v-x)y'
y’ = (v’-1)/(v-x)
(v’-1)/(v-x) (x+v-x)=2
V (v’-1)/(v-x)=2
vv’-v=2(v-x)
vv’-3v=-2x

any help will be very much appreciated.

 

[SteamKing]

Homework Statement

Solve the differential equation:
dy/dx = 2/(x+e^y)

Threads for solving differential equations by nature belong in the Calculus HW forum.

 

[Samy_A]

vv’-3v=-2x

Hmm, this last equation is homogeneous, so setting v=ux should allow you to separate variables.

 

[2nafish117]

fred_91
hi
use this result to simplify it to a linear differential equation
dy/dx=1/(dx/dy)

 

[SammyS]

fred_91
hi
use this result to simplify it to a linear differential equation
dy/dx=1/(dx/dy)

Oh yes! This works very nicely.

Use it with the given D.E.