x^{''}+3x^'+33x=10cos(5t)

Lösung

x^{^{''}} + 3 x^{^{'}} + 33 x = 10 cos (5 t)

x = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{123 t}{2}) + c_{2} sin (\frac{123 t}{2})) + \frac{150}{289} sin (5 t) + \frac{80}{289} cos (5 t)

Schritte zur Lösung

x^{''} (t) + 3 x^{'} (t) + 33 x = 10 cos (5 t)

Solve linear ODE:

x = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{123 t}{2}) + c_{2} sin (\frac{123 t}{2})) + \frac{150}{289} sin (5 t) + \frac{80}{289} cos (5 t)

x = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{123 t}{2}) + c_{2} sin (\frac{123 t}{2})) + \frac{150}{289} sin (5 t) + \frac{80}{289} cos (5 t)

y^{^{''}} + 4 y^{^{'}} + 3 y = 5 e^{- 3 t}

y^{^{'''}} - 2 y^{^{''}} + 5 y^{^{'}} = e^{x} cos (2 x)

(D^{2} - 3 D + 2) (D^{2} + 2 D + 1) y = x

y^{^{''}} - 60 y^{^{'}} - 900 y = 5 e^{10 x}

y^{^{''}} - 16 y = x e^{x}