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Beliebt Rechnen >

y^{'''}+3y^{''}-4y=e^{-2x}

Lösung

y^{^{'''}} + 3 y^{^{''}} - 4 y = e^{- 2 x}

Lösung

y = c_{1} e^{x} + c_{2} e^{- 2 x} + c_{3} x e^{- 2 x} - \frac{e ^{- 2 x} x ^{2}}{6}

Schritte zur Lösung

y^{'''} (x) + 3 y^{''} (x) - 4 y = e^{- 2 x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} + c_{3} x e^{- 2 x} - \frac{e ^{- 2 x} x ^{2}}{6}

y = c_{1} e^{x} + c_{2} e^{- 2 x} + c_{3} x e^{- 2 x} - \frac{e ^{- 2 x} x ^{2}}{6}

Graph

Beliebte Beispiele

y^{''}+y^'-2y+1=0

y^{^{''}} + y^{^{'}} - 2 y + 1 = 0

(d^2y)/(dx^2)-4(dy)/(dx)-12=3cos(x)

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 12 = 3 cos (x)

y^{^{''}} + 4 y = - 1

y^{''}-3y^'+2y=(e^{2x})/(1+e^{2x)}

y^{^{''}} - 3 y^{^{'}} + 2 y = \frac{e ^{2 x}}{1 + e ^{2 x}}

(d^2-2d+2)y=4x-2+2e^xsin(x)

(d^{2} - 2 d + 2) y = 4 x - 2 + 2 e^{x} sin (x)