(d^2y)/(dx^2)-(dy)/(dx)-2y=6x+6e^{-x}

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

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

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

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

\frac{1}{8} y^{^{''}} + 8 x + 4 y^{^{'}} = 0, y^{^{'}} (0) = 9, y (0) = 0

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 1 = 0