I ODE in Excel Calculus Add-In

  • Thread starter jknight291
  • Start date
I am attempting to solve an ODE using a Calculus add-in for Excel. I am an industry professional and I have not even thought about Differential Equations in 8 years. The equation that I am attempting to solve is in the form:

244011
(1)

The ODE solver that I am using solves equations of the form:

244012
(2)

The results that I get by solving equation 1 above using my Excel Add-in for ODEs is a sinusoidal type reaction. However, when I solve numerically I get the expected result.

I think my ODE solver may be solving for
244013
and not just x`1. I tried to transform the results using algebra but the results were still obscure.

I think I may need to transform equation 1 to match the format of equation 2 before solving, but I am not sure. Like I said, it has been several years since taking a DE course so I am little rusty.

Can anyone offer some help?

Thanks!
 
115
42
What is ##x_2##?
 
A nonlinear algebraic equation. I am solving this as a system of equations.
 

pasmith

Homework Helper
1,734
408
To echo @Gaussian97,

What is [itex]x_2[/itex]? Is it a constant? Is it a known function of time? Is there another ODE which governs its evolution over time?

If the ODE solver expects an equation of the form [itex]\dot y = f(t,y)[/itex] then you will need to put your ODE into that form before solving. Now by the chain rule [tex]
\frac{dx_1^{-0.286}}{dt} = -{0.286}x_1^{-1.286}\frac{dx_1}{dt}[/tex] so [tex]
\frac{dx_1}{dt} = -\frac{x_1^{1.286}}{0.286}C(x_1^{-0.286} - x_2^{-0.286}).[/tex]
 

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