Variation of parameters question

**dankelly07** · May 26th 2009, 08:27 AM

Can someone help get me started with this I'm not sure where to begin..

$ \begin{gathered} x\frac{{dy}} {{dx}} + (2 + 3x)\frac{{dy}} {{dx}} + 3y = r(x); \hfill \\ \hfill \\ Solution \hfill \\ y = 1/x \hfill \\ with \hfill \\ r(x) = 0 \hfill \\ \end{gathered} $

Form

$ y(x) = \frac{1} {x}v(x) $

and I need to find the complete general equation corresponding to

$ r(x) = 3e^{ - 3x} $

Can someone get me started with this.. do I differentiate y(x) part and substitute that into the equation?

**HallsofIvy** · May 26th 2009, 12:03 PM

Originally Posted by dankelly07

Can someone help get me started with this I'm not sure where to begin..

$ \begin{gathered} x\frac{{dy}} {{dx}} + (2 + 3x)\frac{{dy}} {{dx}} + 3y = r(x); \hfill \\$

You mean $\frac{d^2y}{dx^2}+ (2+3x)\frac{dy}{dx}+ 3y= r(x)$

$\hfill \\ Solution \hfill \\ y = 1/x \hfill \\ with \hfill \\ r(x) = 0 \hfill \\ \end{gathered} $

Form

$ y(x) = \frac{1} {x}v(x) $

and I need to find the complete general equation corresponding to

$ r(x) = 3e^{ - 3x} $

Can someone get me started with this.. do I differentiate y(x) part and substitute that into the equation?

Because this is a second order equation, you will need two independent solutions to the homogeneous differential equation. Try putting y= v(x)/x into the differential equation. That reduces to a first order, separable equation so that you can find v and then another y solution.

After you you have done that, you can use those solution in variation of parameters.

Thread: Variation of parameters question

LinkBack

Thread Tools

Display

Variation of parameters question

Similar Math Help Forum Discussions

Theoretical question on the Variation of Parameters method

help with variation of parameters question

Variation of Parameters

Variation of Parameters

variation of parameters

Search Tags