- #1
lat77
- 6
- 0
Homework Statement
Solve using an appropriate substitution
ydx+(1+ye^x)dy=0
Homework Equations
N/A
The Attempt at a Solution
u=y
du/dx=dy/dx
u+(1+ue^x)du/dx=0
This is where it gets really sticky for me. I can't see it being a separable variable problem because it seems impossible to separate the u and the x. It also seems very unlikely that it is a linear d.e. or a bernoulli d.e. because the integrating factor would be e^∫(1/(1+ue^x)dx ) which seems impossible to do. The answer is e^(-x)=ylny+cy.