Simplifying an ODE into explicit form

[cooljosh2k2]

Homework Statement

So i think i found the general solutions to both these separable equations, but I am not sure if I am suppose to simplify any further to get it in explicit form, and how i can even do that.

Homework Equations

The Attempt at a Solution

1. \frac{dy}{dx} - \frac{x+e^{-x}}{y+e^{y}} = 0

2. \frac{dx}{dt} = te^{x+t}

For 1), i get \frac{y^{2}}{2}+e^{y} = \frac{x^{2}}{2}-e^{-x}+C

and for 2) i get:

-e^{-x}+C = te^{t}-e^{t}

Are these right? and is there anyway to simplify them into explicit form? Thanks

 

[LCKurtz]

They are both correct. You can't solve the first one for y explicitly with the usual functions. You could solve the second for x if you wanted to using logarithms.