y^{'''}-5y^{''}+6y^'=6e^{2x}-2

Lösung

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 6 e^{2 x} - 2

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

Schritte zur Lösung

y^{'''} (x) - 5 y^{''} (x) + 6 y^{'} (x) = 6 e^{2 x} - 2

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} + y = 4 e^{- x}

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

y^{^{''}} + 9 y^{^{'}} = cos (3 t)

(D^{2} + 2 D + 1) y = x e^{- x}

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