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Beliebt Rechnen >

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

Lösung

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

Lösung

y = e^{\frac{3 x}{2}} (c_{1} cos (\frac{7 x}{2}) + c_{2} sin (\frac{7 x}{2})) + \frac{e ^{x} x}{2} + \frac{1}{4} e^{x}

Schritte zur Lösung

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

Solve linear ODE:

y = e^{\frac{3 x}{2}} (c_{1} cos (\frac{7 x}{2}) + c_{2} sin (\frac{7 x}{2})) + \frac{e ^{x} x}{2} + \frac{1}{4} e^{x}

y = e^{\frac{3 x}{2}} (c_{1} cos (\frac{7 x}{2}) + c_{2} sin (\frac{7 x}{2})) + \frac{e ^{x} x}{2} + \frac{1}{4} e^{x}

Graph

Beliebte Beispiele

derivative of 1(-5x+3(-3x+2))

\frac{d}{d x} (1 (- 5 x + 3) (- 3 x + 2))

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integral of 1/(ln(x))

\int \frac{1}{ln ( x )} d x

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\int \frac{y + 1}{y - 1} d y