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Beliebt Rechnen >

y^{''}-8y^'+20y=200x^2-39xe^x

Lösung

y^{^{''}} - 8 y^{^{'}} + 20 y = 200 x^{2} - 39 x e^{x}

Lösung

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 10 x^{2} + 8 x + \frac{11}{5} - 3 x e^{x} - \frac{18}{13} e^{x}

Schritte zur Lösung

y^{''} (x) - 8 y^{'} (x) + 20 y = 200 x^{2} - 39 x e^{x}

Solve linear ODE:

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 10 x^{2} + 8 x + \frac{11}{5} - 3 x e^{x} - \frac{18}{13} e^{x}

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 10 x^{2} + 8 x + \frac{11}{5} - 3 x e^{x} - \frac{18}{13} e^{x}

Graph

Beliebte Beispiele

integral from 0 to 8 of xe^{-x}

\int_{0}^{8} x e^{- x} d x

derivative of-x/(x^2+y^2)

\frac{d}{d x} (- \frac{x}{x ^{2} + y ^{2}})

integral of 1/(sqrt(2-3x^2))

\int \frac{1}{2 - 3 x ^{2}} d x

limit as x approaches pi-of cot(x)

x \to π - lim (cot (x))

derivative 8e^{4x}

d er i v a t i v e 8 e^{4 x}