Curiosity on second order ODE

02062015, 10:02 AM
(This post was last modified: 02062015 10:28 AM by salvomic.)
Post: #1




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 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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Messages In This Thread 
Curiosity on second order ODE  salvomic  02062015 10:02 AM
RE: Curiosity on second order ODE  parisse  02062015, 11:44 AM
RE: Curiosity on second order ODE  salvomic  02062015, 12:07 PM
RE: Curiosity on second order ODE  salvomic  05132015, 08:13 PM

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