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Beliebt Rechnen >

y^{''}+4y^'+4y=8x

Lösung

y^{^{''}} + 4 y^{^{'}} + 4 y = 8 x

Lösung

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

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 4 y = 8 x

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+4y^'+3y=sin(e^x)

y^{^{''}} + 4 y^{^{'}} + 3 y = sin (e^{x})

y^{''}-y^'-6y=-e^x+12x,y^'(0)=-2,y(0)=1

y^{^{''}} - y^{^{'}} - 6 y = - e^{x} + 12 x, y^{^{'}} (0) = - 2, y (0) = 1

2x^{''}+5x^'+2x=4e^{-2t}-t

2 x^{^{''}} + 5 x^{^{'}} + 2 x = 4 e^{- 2 t} - t

y^{''}-9y=(9t)/(e^{3t)}

y^{^{''}} - 9 y = \frac{9 t}{e ^{3 t}}

(d^2x)/(dt^2)-3(dx)/(dt)+12x=9t

\frac{d ^{2} x}{d t ^{2}} - 3 \frac{d x}{d t} + 12 x = 9 t