- #1

CSteiner

- 31

- 0

here it is:

i'm sure that this was discovered before, but i was just wondering if it had any official name or something.

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- Thread starter CSteiner
- Start date

- #1

CSteiner

- 31

- 0

here it is:

i'm sure that this was discovered before, but i was just wondering if it had any official name or something.

- #2

the_wolfman

- 346

- 48

[itex] y= a e^{-x}\int{ e^x x^n dx}+ Ce^{-x}[/itex]

The integral can be expressed in terms of the incomplete gamma function.

For positive integer [itex] n [/itex] it simplifies to

[itex] \int{ e^x x^n dx}=e^x\left(x^n - n x^{n-1}+n\left(n-1\right)x^{n-2}\dots -1^n n! \right) [/itex]

This will reproduce your solution for the case [itex] C=0 [/itex] .

- #3

CSteiner

- 31

- 0

yes, that's how I derived it. I was just wondering if it had a name.

- #4

Astronuc

Staff Emeritus

Science Advisor

- 20,867

- 4,840

yes, that's how I derived it. I was just wondering if it had a name.

The equation in the OP is a first order linear ordinary differential equation of the general form y' + p(x) y = q(x), with p(x) = 1, q(x) = ax

http://tutorial.math.lamar.edu/Classes/DE/Linear.aspx

http://mathworld.wolfram.com/First-OrderOrdinaryDifferentialEquation.html

There does not appear to be a special name for that particular form. Perhaps there was way back when.

Some named first and second order ordinary differential equations found here:

http://mathworld.wolfram.com/OrdinaryDifferentialEquation.html

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