7316961e-caa7-4784-ad87-d9baab32c415 14 6 9 decimal

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1rst Order Type 2

local definition s F t 0 > assume s t invlaplace maple 11 line ≡

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

UnitStep 1 ≡ UnitLinear t ≡ UnitGrow d t * exp ω * ≡ UnitDecay d t * - exp ω * ≡ UnitSqrt t sqrt ≡ 51 line

1. Laplace of the forcing function q(t) t q t :

s L t q t s laplace maple :

s L 1 s 2^/

2. Dress the solver for Laplace s F Y0 s L + (s * m s 2^* n + / :

3. Instruct Smath wisely with the local definition Y0 m n t fnct s F t 0 > assume s t invlaplace maple 11 line :

4. Export the solution wrt the DE parameters Y0 m n t fnct m n m / sqrt t * cos Y0 * n * + n m / sqrt t * cos m * - n m * /

5. Assign parameters to this "forced DE"

Y0 0 :

m 1 :

n 0.25 :

d 1 :

ω 5 :

t f Y0 m n t fnct :

6. The executable solution from symbolic expansion f(t) t f 8 t 4 sqrt * 8 / sin 2^*

Laplace 1rst order, forced solution

x 0 ≥ ( x 2 e * ≤ ( & x f wild domain if 1 1 sys

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