# first order non-linear equation

• July 12th 2011, 09:38 AM
vonflex1
first order non-linear equation
hi all,

i have the following question puzzling me:

(dy/dx) = 10^(x+y)

how do i solve it?
• July 12th 2011, 09:41 AM
hatsoff
Re: first order non-linear equation
Quote:

Originally Posted by vonflex1
hi all,

i have the following question puzzling me:

(dy/dx) = 10^(x+y)

how do i solve it?

Notice that $\int 10^{-y}dy=\int 10^xdx$.
• July 12th 2011, 12:33 PM
Chandler26
Re: first order non-linear equation
Hello,

Maybe, you can use, that
$10^{-y} = e^{-y \ln 10}~.$

Then you get the simple ODE:

$\frac{d}{dx} \left( -\frac{1}{\ln 10} 10^{-y} \right) = 10^x~.$
• July 13th 2011, 05:12 AM
HallsofIvy
Re: first order non-linear equation
Of course, the first step, which then leads to what hatsoff and Chandler26 said, is to recognize that $10^{x+y}= 10^x10^y$.