Remove["Global`*"]ec1 = y1''[t] == -(1/3) y1[t] + (1/3) (y2[t] - y1[t]); ec2 = y2''[t] == -(1/3) (y2[t] - y1[t]) - (1/3) y2[t];eclapla = LaplaceTransform[{ec1, ec2}, t, s] /. {y1[0] -> 1, y2[0] -> 1, y1'[0] -> 1, y2'[0] -> -1}soltrans = Solve[eclapla, {LaplaceTransform[y1[t], t, s], LaplaceTransform[y2[t], t, s]}] // SimplifyY1[s_] = LaplaceTransform[y1[t], t, s] /. soltrans[[1, 1]]Y2[s_] = LaplaceTransform[y2[t], t, s] /. soltrans[[1, 2]]y1l[t_] = InverseLaplaceTransform[Y1[s], s, t]y2l[t_] = InverseLaplaceTransform[Y2[s], s, t]DSolve[{ec1, ec2, y1[0] == 1, y2[0] == 1, y1'[0] == 1, y2'[0] == -1}, {y1[t], y2[t]}, t]
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1 pensamientos impuros:
Remove["Global`*"]
ec1 = y1''[t] == -(1/3) y1[t] + (1/3) (y2[t] - y1[t]); ec2 =
y2''[t] == -(1/3) (y2[t] - y1[t]) - (1/3) y2[t];
eclapla =
LaplaceTransform[{ec1, ec2}, t, s] /. {y1[0] -> 1, y2[0] -> 1,
y1'[0] -> 1, y2'[0] -> -1}
soltrans =
Solve[eclapla, {LaplaceTransform[y1[t], t, s],
LaplaceTransform[y2[t], t, s]}] // Simplify
Y1[s_] = LaplaceTransform[y1[t], t, s] /. soltrans[[1, 1]]
Y2[s_] = LaplaceTransform[y2[t], t, s] /. soltrans[[1, 2]]
y1l[t_] = InverseLaplaceTransform[Y1[s], s, t]
y2l[t_] = InverseLaplaceTransform[Y2[s], s, t]
DSolve[{ec1, ec2, y1[0] == 1, y2[0] == 1, y1'[0] == 1,
y2'[0] == -1}, {y1[t], y2[t]}, t]
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