y^{''}-6y^'+15y=2sin(3t)

Lösung

y^{^{''}} - 6 y^{^{'}} + 15 y = 2 sin (3 t)

y = e^{3 t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + \frac{1}{30} sin (3 t) + \frac{1}{10} cos (3 t)

Schritte zur Lösung

y^{''} (t) - 6 y^{'} (t) + 15 y = 2 sin (3 t)

Solve linear ODE:

y = e^{3 t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + \frac{1}{30} sin (3 t) + \frac{1}{10} cos (3 t)

y = e^{3 t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + \frac{1}{30} sin (3 t) + \frac{1}{10} cos (3 t)

y^{^{''}} - 3 y^{^{'}} + 2 y = 1, y^{^{'}} (4) = 3

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

y^{^{''}} + 2 y^{^{'}} - 8 y = 36 e^{2 t}

y^{^{''}} + 4 y^{^{'}} + 3 y = - e^{- 6 t}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 6 y^{^{'}} - 7 y = 11 e^{2 x}, y (0) = 1, y^{^{'}} (0) = 1