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Beliebt Rechnen >

y^{''}+2y^'+10y=5xe^{(-2x)}

Lösung

y^{^{''}} + 2 y^{^{'}} + 10 y = 5 x e^{(- 2 x)}

Lösung

y = e^{- x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{e ^{- 2 x} x}{2} + \frac{1}{10} e^{- 2 x}

Schritte zur Lösung

y^{''} (x) + 2 y^{'} (x) + 10 y = 5 x e^{(- 2 x)}

Solve linear ODE:

y = e^{- x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{e ^{- 2 x} x}{2} + \frac{1}{10} e^{- 2 x}

y = e^{- x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{e ^{- 2 x} x}{2} + \frac{1}{10} e^{- 2 x}

Graph

Beliebte Beispiele

derivative 2/(x^3+2)

d er i v a t i v e \frac{2}{x ^{3} + 2}

integral of x^2(x^3+2)^2

\int x^{2} (x^{3} + 2)^{2} d x

integral of-(2200x)/(sqrt(25-x^2))

\int - \frac{2200 x}{25 - x ^{2}} d x

limit as x approaches 0 of xln(x^3)

x \to 0 lim (x ln (x^{3}))

y^{''}+9y^'+14y=0

y^{^{''}} + 9 y^{^{'}} + 14 y = 0