(1/2)y^{''}+y^'+5y=sin(3t)

Lösung

(\frac{1}{2}) y^{^{''}} + y^{^{'}} + 5 y = sin (3 t)

y = e^{- t} (c_{1} cos (3 t) + c_{2} sin (3 t)) + \frac{2}{37} sin (3 t) - \frac{12}{37} cos (3 t)

Schritte zur Lösung

(\frac{1}{2}) y^{''} (t) + y^{'} (t) + 5 y = sin (3 t)

Solve linear ODE:

y = e^{- t} (c_{1} cos (3 t) + c_{2} sin (3 t)) + \frac{2}{37} sin (3 t) - \frac{12}{37} cos (3 t)

y = e^{- t} (c_{1} cos (3 t) + c_{2} sin (3 t)) + \frac{2}{37} sin (3 t) - \frac{12}{37} cos (3 t)

y^{^{''''}} + 25 y^{^{''}} = sin (5 t) + t e^{6 t} + 4

6 y^{^{''}} - 10 y^{^{'}} - 4 y = x + 2

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

y^{^{''}} - y^{^{'}} = x e [x], y (0) = 2, y^{^{'}} (0) = 1

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