b1bb8c6c-0250-4c35-8dbb-4fa40494c23b 8 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Dirac integral ... dummy [x-u]. It results from
Laplace solving 2nd order  ... impulse sqrt(t).
Solution is 5 terms wrt Y0, Y1. Set Y0=Y1=0
the Dirac integral remains in explicit form. x f 815 sqrt 4 sqrt * / (u sqrt x u - 4 / exp * 15 sqrt 24 sqrt * / x u - (* (sin * u 0 x int * :

x f 2 min * ≡

x c 10 x ≤ (x 15 ≤ (& cases :

x f x c *

Reconciliation:

1. This document solves analytically the 2nd homogeneous DE.

It will solve for other q(t) that makes sense ... sqrt(t) happens to

be actually incompatible.

2. From other source(s), the solution is isolated in term of (x-u).

Smath 6179 plots/evaluates this type of integral.

]]>

1 a / 1 ε 2^v 2^+ / v int * - 1 t int ≡ t solve maple v ε / atan ε a * / -

=========================================================

t q t sqrt :

Dirac Integral

s L t q t s laplace maple :

One of the solution contains Dirac Integral. Smath/Maple are not companions for that one. There is sanity between the Maple code Smath 6179 and Mathcad 11 [Maple]

s L π sqrt 2 s 2 nthroot 3^* /

Laplace  anlytic solver 
2nd DE homogeneous
under forcing q(t) s F Y0 s - m - (* Y1 - s L - s 2^s m * + n + (/ (- :

Y0 Y1 m n t fnct s F 0 t < assume s t invlaplace maple :

t f Y0 Y1 m n t fnct :

Y0 0 :

Y1 0 :

m 0.5 - :

n 1 :

t f Le format de la chaîne d'entrée est incorrect.

m n C 14 n * - m 2^+ (/ :

m n t sol_3 m n C - (24 n * m 2^- (sqrt * u sqrt 0.5 m * t u - (* - exp * 0.5 4 n * m 2^- (sqrt * t u - (* sin * u 0 t int * (* :

m n t sol_3 8 u sqrt t u - 4 / exp * 15 sqrt t u - (* 24 sqrt * / sin * u 0 t int * 15 sqrt 4 sqrt * /