Hey all, i gonna share another problem to solve here we go:

Consider the equation

where

prove that the solution is:

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- Oct 26th 2008, 10:36 PMBlack KawairothliteNon-Homogeneous Second grade diff. equation to solve
Hey all, i gonna share another problem to solve here we go:

Consider the equation

where

prove that the solution is:

- Oct 27th 2008, 03:40 AMwhipflip15
I just tried using Laplace transforms but i get a slightly different solution. Almost the same. What method did you use?

- Oct 27th 2008, 05:38 AMHallsofIvy
You are NOT asked to solve the equation. You are given a function and asked to show it is the solution.

If

what is y'(x)? what is y"(x)? What is y(0)? What is y'(0)?

You may want to use

- Oct 27th 2008, 11:00 AMBlack Kawairothlite
characteristic equation of second grade ordinary diff eq. and then parameter variation method... that's the way i think is done

that's cheating lol i know it'd work but u gotta get the solution by solving the diff eq... what if you didn't have the answer........(Giggle) - Nov 4th 2008, 06:53 PMBlack Kawairothlite
well i got the answer few days ago, been busy lately but for the record im gonna post the answer..as usual if im wrong correct me plz... :D

so i got the general solution

so

remember that

then the general solution is:

now i gotta get the particular solution which i got with parameters variation method...

so:

where and are unknown but according to the formula:

;

where

and

then

so

and the particular solution is:

and finally

now the initial values:

so

so

then the solution for the initial values is:

(Nod)(Nerd)