y^{''}-y^'+400y=20sin(20t)

Lösung

y^{^{''}} - y^{^{'}} + 400 y = 20 sin (20 t)

y = e^{\frac{t}{2}} (c_{1} cos (\frac{1599 t}{2}) + c_{2} sin (\frac{1599 t}{2})) + cos (20 t)

Schritte zur Lösung

y^{''} (t) - y^{'} (t) + 400 y = 20 sin (20 t)

Solve linear ODE:

y = e^{\frac{t}{2}} (c_{1} cos (\frac{1599 t}{2}) + c_{2} sin (\frac{1599 t}{2})) + cos (20 t)

y = e^{\frac{t}{2}} (c_{1} cos (\frac{1599 t}{2}) + c_{2} sin (\frac{1599 t}{2})) + cos (20 t)

4 y^{^{''}} - y = x e^{\frac{x}{2}}, y (0) = 1, y^{^{'}} (0) = 0

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

y^{^{''}} - 4 y^{^{'}} - 12 y = 3 x^{2} - 5 x + 4 - 3 e^{- 3 x}

y^{^{''}} + y = 2 e^{x}

y^{^{''}} - y^{^{'}} - 6 y = 15 e^{3 t}, y (0) = 2, y^{^{'}} (0) = - 6