# Solve Differential Equation

• Feb 4th 2008, 01:46 PM
bobak
Solve Differential Equation
Find a solution to the following equation.

$\displaystyle e^{\frac{d^2y}{dx^2}} + e^{\frac{dy}{dx}} + e^{y} = 8$

My thoughts: This question is a joke right? short of guessing i can't think of a way to solve this.

• Feb 4th 2008, 10:51 PM
mr fantastic
Quote:

Originally Posted by bobak
Find a solution to the following equation.

$\displaystyle e^{\frac{d^2y}{dx^2}} + e^{\frac{dy}{dx}} + e^{y} = 8$

My thoughts: This question is a joke right? short of guessing i can't think of a way to solve this.

If you only want a solution, an obvious one is y = k for suitable value of k .... And yes, I did guess (but it was a shrewd guess ..... ;)
• Feb 4th 2008, 11:47 PM
bobak
So y=ln6 is the best solution so far. by the was does this even qualify as a second order differential equation?
• Feb 5th 2008, 12:27 AM
mr fantastic
Quote:

Originally Posted by bobak
So y=ln6 is the best solution so far. by the was does this even qualify as a second order differential equation?

There's probably a special name. It's not Clairaut's equation, but if you look into it, you'll see it's not so unusual to have equations of this form .....

Where'd the question come from, anyway?
• Feb 5th 2008, 12:31 AM
bobak
My math tutor put in on a problem sheet for me, he claims he has a solution to it, I'll ask him what it is later if its is anything other than ln6 I'll post it.
• Feb 5th 2008, 06:16 PM
bnic3029