02-06-2015, 10:02 AM

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

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