y^{'''}+2y^{''}-9y^'-18=10+20sin(5t)

Lösung

y^{^{'''}} + 2 y^{^{''}} - 9 y^{^{'}} - 18 = 10 + 20 sin (5 t)

y = c_{1} + c_{2} e^{(- 1 + 10) t} + c_{3} e^{(- 1 - 10) t} - \frac{5}{157} sin (5 t) + \frac{17}{157} cos (5 t) - \frac{28 t}{9}

Schritte zur Lösung

y^{'''} (t) + 2 y^{''} (t) - 9 y^{'} (t) - 18 = 10 + 20 sin (5 t)

Solve linear ODE:

y = c_{1} + c_{2} e^{(- 1 + 10) t} + c_{3} e^{(- 1 - 10) t} - \frac{5}{157} sin (5 t) + \frac{17}{157} cos (5 t) - \frac{28 t}{9}

y = c_{1} + c_{2} e^{(- 1 + 10) t} + c_{3} e^{(- 1 - 10) t} - \frac{5}{157} sin (5 t) + \frac{17}{157} cos (5 t) - \frac{28 t}{9}

y^{^{''}} + y^{^{'}} - 6 y = x + e^{2 x}

y^{^{''}} + 12 y^{^{'}} + 100 y = 6

y^{^{''}} - 2 y^{^{'}} - 7 y = 3 x^{2}

1 y^{^{''}} + 4 y^{^{'}} + 4 y = \frac{e ^{- 2 x}}{x ^{2}}

y^{^{''}} + y^{^{'}} - 20 y = 3 e^{t}