adedf6db-2735-4c5f-9635-41b6fdee0524 20 4 5 decimal

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

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. OBSERVE: Dirac integral is independent of initials Y0, Y1

s L π sqrt 2 s 2 nthroot 3^* /

s F Y0 s - m - (* Y1 - s L - s 2^s m * + n + (/ (- :

Y0 Y1 m n t fnct s F t 0 > assume s t invlaplace maple 11 line :

t f Y0 Y1 m n t fnct :

Y0 0 :

Y1 0 :

m 0.5 - :

n 1 :

===== Solutions sanity checked Mathcad11/Maple [jmG] and latest Maple [Uni Smath] =====

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

Y0 m n t sol_1 m n C Y0 0.5 m * t * - exp * m 2^* 0.5 4 n * m 2^- (sqrt * t * cos * (* :

Y0 m n t sol_2 m n C - (Y0 m * 0.5 m * t * - exp * 4 n * m 2^- (sqrt * 0.5 4 n * m 2^- (sqrt * t * sin * (* :

Y0 m n t sol_3 m n C - (4 Y0 * 0.5 m * t * - exp * n * 0.5 4 n * m 2^- (sqrt * t * cos * (* :

Y1 m n t sol_4 m n C - (2 Y1 * 0.5 m * t * - exp * 4 n * m 2^- (sqrt * 0.5 4 n * m 2^- (sqrt * t * sin * (* :

m n t sol_5 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 * (* :

Y0 m n t sol_1 Y0 m n t sol_2 + Y0 m n t sol_3 + Y1 m n t sol_4 + m n t sol_5 +

The complete solution Y0 Y1 m n t Sol Y0 m n t sol_1 Y0 m n t sol_2 + Y0 m n t sol_3 + Y1 m n t sol_4 + m n t sol_5 + :

collect native solutions Y0 0 : Y1 0 : m 0.5 - : n 1 : 14 mat t f Y0 Y1 m n t Sol : x c 10 x ≤ (x 15 ≤ (& cases : 31 line

recast Y0, Y1 => y0, y1 y0 1 : y1 1 - : m 0.5 - : n 1 : 14 mat t f1 y0 m n t sol_1 : t f2 y0 m n t sol_2 : t f3 y0 m n t sol_3 : t f4 y1 m n t sol_4 : t f5 m n t sol_5 : 61 sys

m n C 0.2667 -

Dirac integral is independent from initials Y0, Y1

x f x c * x f1 x c * x f2 x c * x f3 x c * x f4 x c * 4 1 sys x f5

n x Φ 1 π / n x * sin x / * :

1001012 -^Φ 31.830989

Dirac Δ(x) completeness

100 x Φ

Mathcad 11: The Dirac Delta is returned from Maple Δ(x) where Δ(0)= ∞ ... Δ(x) = 0 everywhere else

TheIntegralof x Δ x ∞ - ∞ int : 1 ≡