y^{''}-2y^'-8y=10e^{3x}

Lösung

y^{^{''}} - 2 y^{^{'}} - 8 y = 10 e^{3 x}

y = c_{1} e^{4 x} + c_{2} e^{- 2 x} - 2 e^{3 x}

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) - 8 y = 10 e^{3 x}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- 2 x} - 2 e^{3 x}

y = c_{1} e^{4 x} + c_{2} e^{- 2 x} - 2 e^{3 x}

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

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

6 y^{^{''}} + 6 y^{^{'}} + 73 y = 8 cos (4 x)

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 6 y = - e^{x} + 12 x

y^{^{''}} + 2 y^{^{'}} - 3 y = 2 cos (x) - 4 sin (x)