ODE's
10-15-2014, 08:06 PM
Post: #1
 lrdheat Senior Member Posts: 526 Joined: Feb 2014
ODE's
In desolve with ordinary differential equations, the general solution tends to have a mess of numbers and constants multiplying the variables of interest. Is there a way to collapse all of this into single constants to make the result easier to comprehend, more compact? See what happens when using desolve on y'' + y' - 6*y = 10*e^2*x - 18*e^3*x - 6*x - 11.

The answer provided is correct, but requires effort to boil down (on paper in my case) to something like y = G_0*e^2*x + G_1*e^-3*x + 2*x*e^2*x - 3*e^3*x + x + 2
10-16-2014, 12:13 AM
Post: #2
 mlpalacios8 Junior Member Posts: 6 Joined: Sep 2014
RE: ODE's
I deeply fecund your concern Irdheat...

I have more examples.
**See attachments**.

I love the Prime but the ODE could use more power and polish.
The Prime CAS at its core is really powerful. It has solved many equations other calculators can't or get stuck at.
I'm sure this ODE situation can be improved.

Returns a laplace vector as an answer

Friend's TI Nspire CX Cas

Webpage solving ODE

Prime solving the ODE, returns HUGE answer
10-16-2014, 06:03 AM
Post: #3
 parisse Senior Member Posts: 1,051 Joined: Dec 2013
RE: ODE's
For linear ODE with constant coeffs, the answer is expressed with constants that are the value of y and derivatives at x=0.
Y:=desolve(y'' + y' - 6*y = 10*e^2*x - 18*e^3*x - 6*x - 11; normal(subst(Y,x=0));normal(subst(diff(Y,x),x=0));

For x^2*y'-3*x*y-y^2=0, it is an homogeneous equation, and you get the solution as parametric curves. Observe that the nspire misses the solution y=0.
10-16-2014, 07:55 AM (This post was last modified: 10-16-2014 07:55 AM by parisse.)
Post: #4
 parisse Senior Member Posts: 1,051 Joined: Dec 2013
RE: ODE's
P.S.: most of the time you can not express parametric solutions of an homogeneous equation explicitly (i.e. y in terms of x with usual functions).
Here you can, indeed (using Xcas notations)
Y:=desolve(x^2*y'-3*x*y-2y^2=0);
[t]:=solve(Y[1,0]=x, t);
normal(t*x); returns x^3/(c_0^2-x^2)
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