c17a0f03-7df9-4d9c-8d12-982baf4a4c37 2 4 5 decimal

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1. forcing function
2. Laplce of forcing
3. ODE Laplace solver
4. kernel solution t q d t * - exp ω * : s L t q t s laplace maple : s F Y0 s L + (s * m s * n + / : Y0 m n t fnct s F t 0 > assume s t invlaplace maple : 41 sys

Y0 m n t fnct d ω d t * - exp * m * n n t * m / - exp * Y0 * - (* n n t * m / - exp * ω * - (m * n 2^n t * m / - exp * Y0 * + m 2^n - d m * + (* /

Copy/paste the RHS maple ... export solution wrt ODE parameters Y0 m n t sol d ω d t * - exp * m * n n t * m / - exp * Y0 * - (* n n t * m / - exp * ω * - (m * n 2^n t * m / - exp * Y0 * + m 2^n - d m * + (* / :

Y0 0 :

m 1 :

n 0.25 - :

d 1 :

ω 3 :

λ x 0 ≥ (x e 2^≤ (& :

t f Y0 m n t fnct :

Laplace 1rst order, forced solution

x f λ /

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x Cf confrac x convert maple expand, collect/simplify/equate the coefficients ≡

This is the form to plug in Maple "confrac" x Cf K 1 el x X 1 el - K 2 el x X 2 el - K 3 el x X 3 el - K 4 el x X 4 el - K 5 el x X 5 el - K 6 el x X 6 el - K 7 el x X 7 el - K 8 el / + / + / + / + / + / + / + :

... after conversion to J_Frac

0.4661 x * 68.9473 - 3036.8262 1 x 6.7084 + 292.9148 1 x 24.0794 - 250.1117 1 x 20.1842 - (* / + (* / + (* / +

Export... final reduced form after Maple and equated coefficients x reduced 0.4661 x * 68.9473 - 3036.8262 x 6.7084 + 292.9148 x 24.0794 - 250.1117 x 20.1842 - / + / + / + :

x c 111 x ≤ (x 60 ≤ (& cases :

x reduced x c *