/usr/lib/open-axiom/input/exprode.input is in open-axiom-test 1.5.0~svn3056+ds-1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 | )clear all
)set streams calculate 7
-- We will solve y''' = sin(y'') * exp(y) + cos(x)
-- subject to y(0) = 1, y'(0) = 0, y''(0) = 0
y := operator 'y
eq := differentiate(y x, x, 3) - sin differentiate(y x, x, 2) * exp y x
= cos x
seriesSolve(eq, y, x = 0, [1, 0, 0])
-- Airy, isn't it?
airy := differentiate(y x, x, 2) - x * y x
seriesSolve(airy, y, x = 0, [a0, a1])
-- We can solve around other points than x = 0
seriesSolve(airy, y, x = 1, [a0, a1])
-- System of equations for tan(t) and sec(t)
x := operator 'x
eq1 := differentiate(x t, t) = 1 + x(t)**2
eq2 := differentiate(y t, t) = x(t) * y(t)
seriesSolve([eq2, eq1], [x, y], t = 0, [y 0 = 1, x 0 = 0])
-- System of equations for a damped pendulum of mass and length 1:
eq1 := differentiate(x t, t) = y t
eq2 := differentiate(y t, t) = - g * sin(x t) - c * y t
seriesSolve([eq1, eq2], [x, y], t = 0, [y 0 = a, x 0 = b])
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