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Curiosity on second order ODE
02-06-2015, 10:02 AM (This post was last modified: 02-06-2015 10:28 AM by salvomic.)
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Curiosity on second order ODE
hi,
The second order ordinary differential equation y''(x)-y'(x)-6 y(x) = 0 is solved into y(x) = c_1 e^(-2 x)+c_2 e^(3 x).
Why HP Prime give a factor of \( -\frac{1}{5} \) added?
It give \( -\frac{1}{5}e^{-2x}(-3G_0+G_1)+\frac{1}{5}e^{3x}(2G_0+G_1) \)
With substitution of -3G_0+G1=c_1 and 2G_0+G1=c_2 we get the solution, but multiplied by 1/5.

Therefore, if the ODE isn't homogeneous (i.e. like y''(x)-y'(x)-6 y(x) = t*e^(-2t) we get a long expression with -1/15 ... 1/10 ... (try by yourself) instead of a "simply" expression (see here in Wolfamalpha)

I would like to simplify it a bit Smile
Definitely, I would have a method to collect various constants (G_0, G_1...) to have a more compact format, like we do solving manually the equation. Maybe in the future Prime will do the job for us...

Thank you for reply and patience.

Salvo

∫aL√0mic (IT9CLU), HP Prime 50g 41CX 71b 42s 12C 15C - DM42 WP34s :: Prime Soft. Lib
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Curiosity on second order ODE - salvomic - 02-06-2015 10:02 AM



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