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

Lösung

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

x = c_{1} e^{- t} + c_{2} e^{- 2 t} + \frac{9}{20} sin (2 t) - \frac{3}{20} cos (2 t)

Schritte zur Lösung

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

Solve linear ODE:

x = c_{1} e^{- t} + c_{2} e^{- 2 t} + \frac{9}{20} sin (2 t) - \frac{3}{20} cos (2 t)

x = c_{1} e^{- t} + c_{2} e^{- 2 t} + \frac{9}{20} sin (2 t) - \frac{3}{20} cos (2 t)

2 x^{^{''}} + 5 x^{^{'}} + 4 x = 10 r (t)

x^{^{''}} + 6 x^{^{'}} - 4 x = 8 e^{t}

y^{^{''}} + 9 y = 2 cos (3 x) - 3 sin (3 x)

y^{^{''}} - 4 y^{^{'}} + 3 = 0

y^{^{''}} + 3 y = 6 x