Solving ODEs on the TI-89: Tips & Tricks

[enceladus_]

1. Is it possible for the TI-89 to solve Exact Equations?

Ex: (2x-1)dx + (3y+7)dy = 0

I've tried various forms of input, but I cannot find a way for the Calculator to give me a complete answer. My best luck so far was:

(2x-1)x' + (3y+7)y' = 0. The y' part was correct, the x' part was incomplete.

2. I've been reading about how to convert higher order equations into a form that the calculator can solve.

Ex: y''' + 3y'' + 2y' - 5y = sin(2t)

Can be written as:

y'(subscript 3) = 5y(subscript 1) - 2y(subscript 2) -3y(subscript 3) + sin(2t)

How might I enter this into the TI-89?

3. Why does the TI-89 put tan and cot in terms of sin and cos? I have seen rather simple equations turn into complicated messes because of this.

Thanks in advance.

 

[mfb]

Did you try (2x-1) + (3y+7)y' = 0?

$y'_3$? Looks like an unusual notation. What is wrong with y'''?

 

[enceladus_]

Your suggestion worked, I find it odd that leaving out x' makes it work though.

The TI-89 can only do DE's up to the second degree. Would it help if I explained the method in full?

Thanks for your help.

 

[mfb]

The TI-89 can only do DE's up to the second degree.

Hmm... can it solve coupled DEs?

z=y', z''+3z'+2z-5y=sin(2t)

Your suggestion worked, I find it odd that leaving out x' makes it work though.

dx/dx=1

 

[enceladus_]

Hmm... can it solve coupled DEs?

z=y', z''+3z'+2z-5y=sin(2t)

No, it can't. I see what you're doing though, and its very similar to the method I am trying to use. In my method:

y1 = y, y2 = y', y3 = y''...yn = y ^(n-1).

From these:

y'1 = y' = y2, y'2 = y'' = y3...y'(n) = y^n.

This gives the system:

y'1 = y2
y'2 = y3

My example from earlier:

Ex: y''' + 3y'' + 2y' - 5y = sin(2t)

Can be written as:

y'(subscript 3) = 5y(subscript 1) - 2y(subscript 2) -3y(subscript 3) + sin(2t)

I'm puzzled as to how to enter this in the calculator though.

 

[enceladus_]

I understand I could graph this, but how would that help me?