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.