y^{''}+4y^'+12y=80sin(2x)

Lösung

y^{^{''}} + 4 y^{^{'}} + 12 y = 80 sin (2 x)

y = e^{- 2 x} (c_{1} cos (2^{1 + \frac{1}{2}} x) + c_{2} sin (2^{1 + \frac{1}{2}} x)) + 5 sin (2 x) - 5 cos (2 x)

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 12 y = 80 sin (2 x)

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (2^{1 + \frac{1}{2}} x) + c_{2} sin (2^{1 + \frac{1}{2}} x)) + 5 sin (2 x) - 5 cos (2 x)

y = e^{- 2 x} (c_{1} cos (2^{1 + \frac{1}{2}} x) + c_{2} sin (2^{1 + \frac{1}{2}} x)) + 5 sin (2 x) - 5 cos (2 x)

\frac{d ^{2} y}{d t ^{2}} + \frac{3}{100} \frac{d y}{d t} = 12

y^{^{''}} = - y + cos (2 t)

y^{^{''}} + 5 y^{^{'}} + 2 = 0

y^{^{''}} + 10 y = 10 e^{11 x}

y^{^{''}} + 36 y = 33 cos (5 t), y (0) = 0, y^{^{'}} (0) = 0