1d71d995-a5ef-43fb-92e7-49b885c6be5c 25 4 5 decimal

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Laplace DE solvers from Mathcad 11 => Smath

The sources of this Smath document, conversion from Mathcad 11.

Sokolnifoff & Redheffer is the book I passed exams with the University of California [Berkeley Extension] I still consult this most precious book !

"Institut Technique Professionnel" was a correspon- dance by post school in Paris. Great stuff too ! "Mercier" is also top in Engoineering maths. These two don't exist anymore.

1. Solve the forcing function q(t)

t q t 1 + (e 3 t * -^* :

s L t q t s laplace maple :

s L 3 s + 3 s + (2^+ 3 s + (3^/

2. Dress the solver for Laplace

Y0 - s L - m s * n s / + / (- Y0 s L + (s * m s 2^* n + / ≡

<= Recast the model from source, Maple likes "expression" F(s) in Laplace work.

s F Y0 s L + (s * m s 2^* n + / :

3. Instruct Smath wisely with the local definition

Y0 m n t fnct't' t 11 line : s F s't' invlaplace maple 21 line :

<= A most gorgeous instruction ! The blue comes by default in typing t' .... then back 't'

4. Export the solution wrt the DE parameters

Y0 m n t fnct n m / sqrt t * cos 2 n 19 Y0 * + (* 18 m * + (* 81 m * Y0 * + (m * Y0 n 2^* + (* - m n m / sqrt n m / sqrt t * sin * n 15 m * + (* - 23 t * - exp * n * + 363 t * - exp * m * + (* + 3 t * 3 t * - exp * n 9 m * + (* m * + n 9 m * + (2^m * / -

5. Assign parameters to this "forced DE"

m 1 :

n 16 - :

Y0 0 :

t f Y0 m n t fnct :

6. The executable solution from symbolic expansion f(t)

t f 44 t * exp 3 t * - exp - (* 21 t * 3 t * - exp * + 49 /

Laplace 1rst order, forced solution

x 0 ≥ ( x 1.25 ≤ ( & x f NOT a DE solution if

x sol 44 x * exp 3 x * - exp - (* 21 x * 3 x * - exp * + 49 / :

Note: X_Y plot refuses to understand something in there ! Don't attempt to plot sol(x): it crashes Smath. Maybe too much for X_Y plot ?

The forcing function in this DE

x 0 ≥ ( x 1.25 ≤ ( & x L NOT a DE solution if