43y^{'''}-13y^{''}+42y^'=0

Lösung

43 y^{^{'''}} - 13 y^{^{''}} + 42 y^{^{'}} = 0

y = c_{1} + e^{\frac{13 t}{86}} (c_{2} cos (\frac{7055 t}{86}) + c_{3} sin (\frac{7055 t}{86}))

Schritte zur Lösung

43 y^{'''} (t) - 13 y^{''} (t) + 42 y^{'} (t) = 0

Solve linear ODE:

y = c_{1} + e^{\frac{13 t}{86}} (c_{2} cos (\frac{7055 t}{86}) + c_{3} sin (\frac{7055 t}{86}))

y = c_{1} + e^{\frac{13 t}{86}} (c_{2} cos (\frac{7055 t}{86}) + c_{3} sin (\frac{7055 t}{86}))

y^{^{''}} - 5 y^{^{'}} - 6 y = 0, y (0) = 3, y^{^{'}} (0) = - 3

12 y^{^{''}} - 13 y^{^{'}} + y = 0, y (0) = 12, y^{^{'}} (0) = \frac{1}{12}

16 y^{^{''}} + 12 y^{^{'}} + 9 y = 0

2 y^{^{''}} + y^{^{'}} - y = 0, y (0) = 1, y^{^{'}} (0) = 0

(D^{2} - 9 D + 18) y = 0