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Beliebt Rechnen >

y^{''}+4y^'+5y=15x+e^{(-x)}

Lösung

y^{^{''}} + 4 y^{^{'}} + 5 y = 15 x + e^{(- x)}

Lösung

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + 3 x - \frac{12}{5} + \frac{1}{2} e^{- x}

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 5 y = 15 x + e^{(- x)}

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + 3 x - \frac{12}{5} + \frac{1}{2} e^{- x}

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + 3 x - \frac{12}{5} + \frac{1}{2} e^{- x}

Graph

Beliebte Beispiele

y^{^{'}} = 2 x e^{(2 y)}

inverselaplace 3/(s*(s^2+2s+5))

in v erse l a pl a ce \frac{3}{s \cdot ( s ^{2} + 2 s + 5 )}

integral from 0 to 2pi of cos(x)cos(2x)

\int_{0}^{2 π} cos (x) cos (2 x) d x

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\int sin^{3} (x) cos^{8} (x) d x

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

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