y^{''}+4y^'+13y=-2sin(3t)

Lösung

y^{^{''}} + 4 y^{^{'}} + 13 y = - 2 sin (3 t)

y = e^{- 2 t} (c_{1} cos (3 t) + c_{2} sin (3 t)) - \frac{1}{20} sin (3 t) + \frac{3}{20} cos (3 t)

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) + 13 y = - 2 sin (3 t)

Solve linear ODE:

y = e^{- 2 t} (c_{1} cos (3 t) + c_{2} sin (3 t)) - \frac{1}{20} sin (3 t) + \frac{3}{20} cos (3 t)

y = e^{- 2 t} (c_{1} cos (3 t) + c_{2} sin (3 t)) - \frac{1}{20} sin (3 t) + \frac{3}{20} cos (3 t)

2 y^{^{''}} + 3 y - 2 y = 6 x^{2} + 5 x - 8

\frac{3}{2} \frac{d ^{2} y}{d x ^{2}} + \frac{1}{80} \frac{d y}{d x} = g

x^{^{''}} + 2 x^{^{'}} + 5 x = e^{t}

y^{^{''}} + 40 y^{^{'}} + 4000 y = 800 sin (40 x)

y^{^{''}} + y^{^{'}} = e^{x} cos (x)