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

Lösung

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

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

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) + 5 y = 1

Solve linear ODE:

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

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

10 y^{^{''}} + 45 y^{^{'}} + 2500 y = 180 cos (7 π x)

y^{^{''}} + 4 y = sin (t), y (0) = 1, y^{^{'}} (0) = - 1

y^{^{'''}} + y^{^{''}} - 2 y = x e^{x} + 15

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} + \frac{1}{4} y = x e^{\frac{x}{2}}

x^{^{''}} + 4 x = sin (t)