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Beliebt Rechnen >

y^{'''}+15y^{''}-500y=e^{-10x}

Lösung

y^{^{'''}} + 15 y^{^{''}} - 500 y = e^{- 10 x}

Lösung

y = c_{1} e^{5 x} + c_{2} e^{- 10 x} + c_{3} x e^{- 10 x} - \frac{e ^{- 10 x} x ^{2}}{30}

Schritte zur Lösung

y^{'''} (x) + 15 y^{''} (x) - 500 y = e^{- 10 x}

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{- 10 x} + c_{3} x e^{- 10 x} - \frac{e ^{- 10 x} x ^{2}}{30}

y = c_{1} e^{5 x} + c_{2} e^{- 10 x} + c_{3} x e^{- 10 x} - \frac{e ^{- 10 x} x ^{2}}{30}

Graph

Beliebte Beispiele

(D^2-D)y=e^xcos(x)

(D^{2} - D) y = e^{x} cos (x)

y^{''}+4y=2,y(0)=0,y^'(0)=0

y^{^{''}} + 4 y = 2, y (0) = 0, y^{^{'}} (0) = 0

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

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

y^{''}-y^'+1/4 y=xe^{x/2}

y^{^{''}} - y^{^{'}} + \frac{1}{4} y = x e^{\frac{x}{2}}

4 x^{^{''}} - 2 x = 7