x^{''}+3x^'+2x=sin(3t)

Lösung

x^{^{''}} + 3 x^{^{'}} + 2 x = sin (3 t)

x = c_{1} e^{- t} + c_{2} e^{- 2 t} - \frac{7}{130} sin (3 t) - \frac{9}{130} cos (3 t)

Schritte zur Lösung

x^{''} (t) + 3 x^{'} (t) + 2 x = sin (3 t)

Solve linear ODE:

x = c_{1} e^{- t} + c_{2} e^{- 2 t} - \frac{7}{130} sin (3 t) - \frac{9}{130} cos (3 t)

x = c_{1} e^{- t} + c_{2} e^{- 2 t} - \frac{7}{130} sin (3 t) - \frac{9}{130} cos (3 t)

x^{^{''}} + 8 x^{^{'}} + 16 = 0

x^{^{''''}} - x^{^{''}} = 1

y^{^{''}} - 2 y^{^{'}} + y = 3 e^{t}, y (0) = 1, y^{^{'}} (0) = 1

y^{^{''}} - 4 y^{^{'}} - 5 y = 125

y^{^{''}} + 4 y = 4