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Beliebt Rechnen >

y^{''}-3y^'+7y=xe^x

Lösung

y^{^{''}} - 3 y^{^{'}} + 7 y = x e^{x}

Lösung

y = e^{\frac{3 x}{2}} (c_{1} cos (\frac{19 x}{2}) + c_{2} sin (\frac{19 x}{2})) + \frac{e ^{x} x}{5} + \frac{1}{25} e^{x}

Schritte zur Lösung

y^{''} (x) - 3 y^{'} (x) + 7 y = x e^{x}

Solve linear ODE:

y = e^{\frac{3 x}{2}} (c_{1} cos (\frac{19 x}{2}) + c_{2} sin (\frac{19 x}{2})) + \frac{e ^{x} x}{5} + \frac{1}{25} e^{x}

y = e^{\frac{3 x}{2}} (c_{1} cos (\frac{19 x}{2}) + c_{2} sin (\frac{19 x}{2})) + \frac{e ^{x} x}{5} + \frac{1}{25} e^{x}

Graph

Beliebte Beispiele

derivative 3x^2

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

integral of (2x+1)^7

\int (2 x + 1)^{7} d x

derivative of ln^2(sin(2x))

\frac{d}{d x} (ln^{2} (sin (2 x)))

derivative sqrt(10-x)

d er i v a t i v e 10 - x

limit as x approaches infinity of e^x

x \to \infty lim (e^{x})