<p> export the solution wrt DE parameters </p>

9c4ac7a4-a042-407b-b8ba-48e10d119e59 18 4 5 decimal

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

2nd Order Type 3

UnitStep 1 ≡ UnitLinear t ≡ UnitGrow d t * exp ω * ≡ UnitDecay d t * - exp ω * ≡ Fails Dirac Integral t sqrt ≡ 51 line

t ω d q 1 :

s ω d L t ω d q t s laplace maple :

s ω d L 1 s /

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

Laplace solver ODE2 normalised c/w forcing function, parameters and initial conditions.

solution is wild wrt parameters and assigned to a function wrt parameters. Y0 Y1 m n ω t fnct s F t 0 > assume s t invlaplace maple 11 line :

<p> export the solution wrt DE parameters </p>

Export the solution wrt the DE parameters  ... a long expansion that will solve for any [Y0,Y1, m,n] Y0 Y1 m n ω t fnct n 221 m t * 2 / - exp 4 n * m 2^- sqrt t * 2 / cos * 1 - n Y0 * + (* + (* m t * 2 / - exp Y1 * 4 n * m 2^- sqrt t * 2 / sin * 4 n * m 2^- sqrt * + (* m t * 2 / - exp Y0 * m 2^* 4 n * m 2^- sqrt t * 2 / cos * - m t * 2 / - exp m * Y0 * 4 n * m 2^- sqrt t * 2 / sin * 4 n * m 2^- sqrt * + (* - m 2^1 m t * 2 / - exp 4 n * m 2^- sqrt t * 2 / cos * - (* + m t * 2 / - exp m * 4 n * m 2^- sqrt t * 2 / sin * 4 n * m 2^- sqrt * + 4 n * m 2^- (n * / -

Y0 0 :

Y1 0 :

m 0.5 :

n 1.5 :

d 0.5 :

ω 1 :

The RHS algorithm is the solution
wrt user parameters, assigned f(t) t f Y0 Y1 m n ω t fnct :

Export this elegant user solution ... Optimiz: NONE ... copy/paste the RHS t f 23 / 23 - (12 /^412 /^* 114 / - 23 - (12 /^412 /^* 8 / + (t * exp * 14 / - 23 - (12 /^412 /^* 8 / + / 114 / - 23 - (12 /^412 /^* 8 / - (t * exp * 14 / - 23 - (12 /^412 /^* 8 / - / - (* 23 / -

1. exp(-d*x)*ω generalised decay 2. exp(d*x)*ω generalised grow 3. ω=1 ... UnitGrow/UnitDecay 4. 'd' sets the shape

d x * exp ω * d x * - exp ω * 2 1 sys

Observe: in the conditional the text "" blanks the trace ... same as Mathcad .

x f x 0 ≥ ( x 10 ≤ ( & cases 2 3 / 2 1 sys