hi all,

i have the following question puzzling me:

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

how do i solve it?

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- Jul 12th 2011, 09:38 AMvonflex1first order non-linear equation
hi all,

i have the following question puzzling me:

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

how do i solve it? - Jul 12th 2011, 09:41 AMhatsoffRe: first order non-linear equation
- Jul 12th 2011, 12:33 PMChandler26Re: first order non-linear equation
Hello,

Maybe, you can use, that

$\displaystyle 10^{-y} = e^{-y \ln 10}~.$

Then you get the simple ODE:

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