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Beliebt Rechnen >

(D^4+2D^3+2D^2)y=2xe^{-x}

Lösung

(D^{4} + 2 D^{3} + 2 D^{2}) y = 2 x e^{- x}

Lösung

y = c_{1} + c_{2} x + e^{- x} (c_{3} cos (x) + c_{4} sin (x)) + 2 e^{- x} x + 4 e^{- x}

Schritte zur Lösung

(D^{4} + 2 D^{3} + 2 D^{2}) y = 2 x e^{- x}

Solve linear ODE:

y = c_{1} + c_{2} x + e^{- x} (c_{3} cos (x) + c_{4} sin (x)) + 2 e^{- x} x + 4 e^{- x}

y = c_{1} + c_{2} x + e^{- x} (c_{3} cos (x) + c_{4} sin (x)) + 2 e^{- x} x + 4 e^{- x}

Graph

Beliebte Beispiele

(d^2y)/(dx^2)+4(dy)/(dx)-12=0

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} - 12 = 0

y^{''}+9y=t^2e^{3t}

y^{^{''}} + 9 y = t^{2} e^{3 t}

y^{''}+16y=8cos(4x)+12sin(4x)

y^{^{''}} + 16 y = 8 cos (4 x) + 12 sin (4 x)

(d^2x)/(dt^2)+9x=5sin(3t)

\frac{d ^{2} x}{d t ^{2}} + 9 x = 5 sin (3 t)

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

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