y^{''}+y^'+64y=5cos(2t)

Lösung

y^{^{''}} + y^{^{'}} + 64 y = 5 cos (2 t)

y = e^{- \frac{t}{2}} (c_{1} cos (\frac{255 t}{2}) + c_{2} sin (\frac{255 t}{2})) + \frac{5}{1802} sin (2 t) + \frac{75}{901} cos (2 t)

Schritte zur Lösung

y^{''} (t) + y^{'} (t) + 64 y = 5 cos (2 t)

Solve linear ODE:

y = e^{- \frac{t}{2}} (c_{1} cos (\frac{255 t}{2}) + c_{2} sin (\frac{255 t}{2})) + \frac{5}{1802} sin (2 t) + \frac{75}{901} cos (2 t)

y = e^{- \frac{t}{2}} (c_{1} cos (\frac{255 t}{2}) + c_{2} sin (\frac{255 t}{2})) + \frac{5}{1802} sin (2 t) + \frac{75}{901} cos (2 t)

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

y^{^{''}} - y^{^{'}} + 14 y = \frac{4 + e x}{2}

y^{^{''}} - 2 y^{^{'}} + 3 y = 2

y^{^{'''}} + 2 y^{^{''}} - 5 y^{^{'}} - 6 y = sin (6 t)

y^{^{''}} + 9 y = 7 sec (3 x)