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Problem statement

ode t w t 2 diff ω 2^t w * + 0 ≡ :

ic 0 w 1 ≡ t w t diff t 0 ≡ at 1 ≡ 21 sys :

Solution with complex exponentials in two steps

dsol ode t w t ODE.2 : dsol Assign t w 31 line k2 k1 e 2 i * t * ω *^* + e i t * ω *^/

Notice that ODE is true

ode 1

sol ic k1 k2 21 sys Solve : sol Assign t w 31 line i 1 - i ω * + 1 i ω * + (e 2 i * t * ω *^* + (* 2 ω * e i t * ω *^* / -

Applying ic conditions.

ω 1 :

x w Re

Plot with a numerical ω

Use Re(w)

k1 Re 0.5

k2 Re 0.5

Solution with reals sin and cosin: same two steps, but with assume

t w k1 k2 ω Clear 1

ω 0 > assume Maxima ω 0 > 11 sys

dsol ode t w t ODE.2 : dsol Assign t w 31 line k1 t ω * sin * k2 t ω * cos * +

ode 1

sol ic k1 k2 21 sys Solve : sol Assign t w 31 line t ω * sin t ω * cos ω * + ω /

ω 1 :

x w

Plot

k1 1

k2 1

Kill Maxima variables, for re-evaluations at the begin of this file:

all kill Maxima done

Alvaro