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Beliebt Rechnen >

y^{''}-4y^'+8y=x^3-x

Lösung

y^{^{''}} - 4 y^{^{'}} + 8 y = x^{3} - x

Lösung

y = e^{2 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{x ^{3}}{8} + \frac{3 x ^{2}}{16} - \frac{x}{32} - \frac{1}{16}

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) + 8 y = x^{3} - x

Solve linear ODE:

y = e^{2 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{x ^{3}}{8} + \frac{3 x ^{2}}{16} - \frac{x}{32} - \frac{1}{16}

y = e^{2 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{x ^{3}}{8} + \frac{3 x ^{2}}{16} - \frac{x}{32} - \frac{1}{16}

Graph

Beliebte Beispiele

y^{''}-4y^'+4y= 1/x e^{2x}

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

y^{''}-4y^'+4y=(e^{-2x})/(x^2)

y^{^{''}} - 4 y^{^{'}} + 4 y = \frac{e ^{- 2 x}}{x ^{2}}

y^{''}-2y^'+y=-6e^t

y^{^{''}} - 2 y^{^{'}} + y = - 6 e^{t}

4y^{''}-6y^'+7y=8

4 y^{^{''}} - 6 y^{^{'}} + 7 y = 8

(4D^2-4D+1)y=100

(4 D^{2} - 4 D + 1) y = 100