y^{''}+4y^'+3y=30e^{2t}

Lösung

y^{^{''}} + 4 y^{^{'}} + 3 y = 30 e^{2 t}

y = c_{1} e^{- t} + c_{2} e^{- 3 t} + 2 e^{2 t}

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) + 3 y = 30 e^{2 t}

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{- 3 t} + 2 e^{2 t}

y = c_{1} e^{- t} + c_{2} e^{- 3 t} + 2 e^{2 t}

y^{^{''}} + 25 y = 14 cos (5 x) + 21 sin (5 x)

l in e a r y^{^{''}} - y = t, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{2} x (cos (x) - 4 sin (x))

y^{^{''}} - y^{^{'}} = 5 e^{2 x}

y^{^{''}} - y - 2 y = 1 + t