y^{'''}-2y^'-4y=25sin(x)

Lösung

y^{^{'''}} - 2 y^{^{'}} - 4 y = 25 sin (x)

y = c_{1} e^{2 x} + e^{- x} (c_{2} cos (x) + c_{3} sin (x)) - 4 sin (x) + 3 cos (x)

Schritte zur Lösung

y^{'''} (x) - 2 y^{'} (x) - 4 y = 25 sin (x)

Solve linear ODE:

y = c_{1} e^{2 x} + e^{- x} (c_{2} cos (x) + c_{3} sin (x)) - 4 sin (x) + 3 cos (x)

y = c_{1} e^{2 x} + e^{- x} (c_{2} cos (x) + c_{3} sin (x)) - 4 sin (x) + 3 cos (x)

y^{^{''}} + 5 y^{^{'}} + 4 y = 1, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - y^{^{'}} + 400 y = 20 sin (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}