x^{''}+3x^'+33x=8cos(5t)

Lösung

x^{^{''}} + 3 x^{^{'}} + 33 x = 8 cos (5 t)

x = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{123 t}{2}) + c_{2} sin (\frac{123 t}{2})) + \frac{120}{289} sin (5 t) + \frac{64}{289} cos (5 t)

Schritte zur Lösung

x^{''} (t) + 3 x^{'} (t) + 33 x = 8 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{120}{289} sin (5 t) + \frac{64}{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{120}{289} sin (5 t) + \frac{64}{289} cos (5 t)

x^{^{''}} + 16 x = cos (4 t)

y^{^{''}} - 4 y^{^{'}} + 4 y = x^{3} e^{2 x}

y^{^{''}} + 4 y = - 12 sin (2 x), y (0) = 1.8, y^{^{'}} (0) = 5

y^{^{''}} - 11 y^{^{'}} + 24 y = 13 + 24 x

y^{^{''}} + 2 y^{^{'}} + 2 y = sin (t), y (0) = 0, y^{^{'}} (0) = 0