Integral of inhomogenous dif equation

**moolimanj** · February 15th 2008, 01:44 AM

Hi all

Can someone please help me find the solution to this question please?

**mr fantastic** · February 15th 2008, 01:49 AM

Originally Posted by moolimanj

Hi all

Can someone please help me find the solution to this question please?

There's a standard process to follow. Where in this process are you stuck?

**moolimanj** · February 15th 2008, 02:48 AM

Its the x^2 term thats causing me grief.

Is the solution still of the form: y=p1x+p0

**mr fantastic** · February 15th 2008, 03:00 AM

Originally Posted by moolimanj

Its the x^2 term thats causing me grief.

Is the solution still of the form: y=p1x+p0

You try to get a particular solution of the form $y = p_2 x^2 + p_1 x + p_0$ where the values of $p_2 \,$ , $p_1\,$ and $p_0 \,$ have to be found.

Substitute the particular solution into the DE:

$5 (2 p_2) + 4(2 p_2 x + p_1) + (p_2 x^2 + p_1 x + p_0) = x^2$

$\Rightarrow p_2 x^2 + x(8p_2 + p_1) + (10p_2 + 4p_1 + p_0) = x^2$

Equate coefficients of powers of x:

$p_2 = 1$ .... (1)

$8p_2 + p_1 = 0$ .... (2)

$10p_2 + 4p_1 + p_0 = 0$ .... (3)

So a particular solution is $y = x^2 - 8x + 22$ .

Now add this particular solution to the homogenous solution to get the general solution.

Thread: Integral of inhomogenous dif equation

LinkBack

Thread Tools

Display

Integral of inhomogenous dif equation

Similar Math Help Forum Discussions

[SOLVED] Inhomogenous differential Equations

inhomogenous eqn

inhomogenous d .e

Inhomogenous D.e,,help needed!

differential inhomogenous????help

Search Tags