# Math Help - first order non-linear equation

1. ## first order non-linear equation

hi all,

i have the following question puzzling me:

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

how do i solve it?

2. ## Re: first order non-linear equation

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 $\int 10^{-y}dy=\int 10^xdx$.

3. ## Re: first order non-linear equation

Hello,

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

Then you get the simple ODE:

$\frac{d}{dx} \left( -\frac{1}{\ln 10} 10^{-y} \right) = 10^x~.$

4. ## Re: first order non-linear equation

Of course, the first step, which then leads to what hatsoff and Chandler26 said, is to recognize that $10^{x+y}= 10^x10^y$.