y^{''}+100y^'+2500y=20

Lösung

y^{^{''}} + 100 y^{^{'}} + 2500 y = 20

y = c_{1} e^{- 50 t} + c_{2} t e^{- 50 t} + \frac{1}{125}

Schritte zur Lösung

y^{''} (t) + 100 y^{'} (t) + 2500 y = 20

Solve linear ODE:

y = c_{1} e^{- 50 t} + c_{2} t e^{- 50 t} + \frac{1}{125}

y = c_{1} e^{- 50 t} + c_{2} t e^{- 50 t} + \frac{1}{125}

y^{^{''}} - y^{^{'}} - 2 y = 4

y^{^{''}} - 4 y^{^{'}} - y - 2 = 0

x^{^{''}} + 4 x = 10 cos (3 t)

y^{^{''}} + 9 y = 12 x e^{2 x}

y^{^{''}} - y^{^{'}} - 2 y = 7 e^{2 x} - 3 e^{x}