0.25y^{''}+0.25y^'+16y=5cos(2t)

Lösung

0.25 y^{^{''}} + 0.25 y^{^{'}} + 16 y = 5 cos (2 t)

y = e^{- \frac{t}{2}} (c_{1} cos (\frac{255 t}{2}) + c_{2} sin (\frac{255 t}{2})) + 0.01109 \dots sin (2 t) + \frac{300}{901} cos (2 t)

Schritte zur Lösung

0.25 y^{''} (t) + 0.25 y^{'} (t) + 16 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})) + 0.01109 \dots sin (2 t) + \frac{300}{901} cos (2 t)

y = e^{- \frac{t}{2}} (c_{1} cos (\frac{255 t}{2}) + c_{2} sin (\frac{255 t}{2})) + 0.01109 \dots sin (2 t) + \frac{300}{901} cos (2 t)

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

y^{^{''}} + 9 y = sin (2.9 t), y (0) = 1, y^{^{'}} (0) = 1

y^{^{''}} + 4 y = 11 sec^{2} (2 t)

y^{^{''}} - 5 y^{^{'}} + 4 y = 2 e^{x} + x + 1

4 y^{^{''}} - 8 y^{^{'}} + 3 = 0, y (0) = 2, y^{^{'}} (0) = \frac{1}{2}