The equation is:

dy/dx=y+2

The answer is y=Ce^{x}-2

Can anyone explain this?

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- Mar 28th 2012, 12:06 PMDeo3560y`=y+2 Seems Simple, but i can't match the answer up to it.
The equation is:

dy/dx=y+2

The answer is y=Ce^{x}-2

Can anyone explain this? - Mar 28th 2012, 12:42 PMRidleyRe: y`=y+2 Seems Simple, but i can't match the answer up to it.
The answer looks correct. You can easily check if it's correct yourself by finding the derivative and plugging it back into the equation.

- Mar 29th 2012, 09:35 AMthelostchildRe: y`=y+2 Seems Simple, but i can't match the answer up to it.
If you also want to see why write

the equation is seperable and can be written as

$\displaystyle \int \frac{dy}{y+2} = \int dx$

so

$\displaystyle \ln (y+2) = x + c $

then taxing the exp of both sides and writing the arbitrary constant as C = ln c gives the solution as you have it - Mar 30th 2012, 03:38 PMCreebeRe: y`=y+2 Seems Simple, but i can't match the answer up to it.
Or you can check the answer by taking the derivative of it:

$\displaystyle \frac{d}{dx} y(x) = Ce^x$

So you put this back into the differential equation:

$\displaystyle Ce^x = [Ce^x - 2] + 2$

It turns out to be true.