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Beliebt Rechnen >

(D^2-3D+2)(D^2+2D+1)y=x

Lösung

(D^{2} - 3 D + 2) (D^{2} + 2 D + 1) y = x

Lösung

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

Schritte zur Lösung

(D^{2} - 3 D + 2) (D^{2} + 2 D + 1) y = x

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}-60y^'-900y=5e^{10x}

y^{^{''}} - 60 y^{^{'}} - 900 y = 5 e^{10 x}

y^{''}-16y=xe^x

y^{^{''}} - 16 y = x e^{x}

(d^2y)/(dx^2)+c^2y=sec^2(cx)

\frac{d ^{2} y}{d x ^{2}} + c^{2} y = sec^{2} (c x)

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

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

y^{''}-8y^'+16y=24x+2,y(0)=2,y^'(0)=-1

y^{^{''}} - 8 y^{^{'}} + 16 y = 24 x + 2, y (0) = 2, y^{^{'}} (0) = - 1