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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} - y^{^{'}} = 4 x e^{x}, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 10 y^{^{'}} + 61 y = 5 cos (7 t)

(D^{4} - 1) y = 7 x^{2}

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{5 x}

y^{^{'''}} - y = 1