y^{''}-2y^'-3y=3e^{5t}

Lösung

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 e^{5 t}

y = c_{1} e^{3 t} + c_{2} e^{- t} + \frac{1}{4} e^{5 t}

Schritte zur Lösung

y^{''} (t) - 2 y^{'} (t) - 3 y = 3 e^{5 t}

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- t} + \frac{1}{4} e^{5 t}

y = c_{1} e^{3 t} + c_{2} e^{- t} + \frac{1}{4} e^{5 t}

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} - 5 y = 24 e^{x}

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 3 y = 6 x^{2} + 19 x + 5

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

y^{^{''}} + 4 y^{^{'}} = sec (2 x)

y^{^{''}} + y = 2 e^{- x}, y (0) = 0, y^{^{'}} (0) = 0