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Beliebt Rechnen >

(d^2y)/(dx^2)+2(dy)/(dx)-8y=0

Lösung

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 8 y = 0

Lösung

y = c_{1} e^{2 x} + c_{2} e^{- 4 x}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 8 y = 0

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 4 x}

y = c_{1} e^{2 x} + c_{2} e^{- 4 x}

Graph

Beliebte Beispiele

(d^2y)/(dx^2)-2*(dy)/(dx)=0

\frac{d ^{2} y}{d x ^{2}} - 2 \cdot \frac{d y}{d x} = 0

16y^{''}-40y^'+25y=0,y(0)=3,y(0)=-9/4

16 y^{^{''}} - 40 y^{^{'}} + 25 y = 0, y (0) = 3, y (0) = - \frac{9}{4}

(d^2y)/(dx^2)=a(dy)/(dx)

\frac{d ^{2} y}{d x ^{2}} = a \frac{d y}{d x}

(d^2y)/(dx^2)-2(dy)/(dx)-2y=0

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} - 2 y = 0

y^{''}+2y^'+37y=0,y(0)=2,y^'(0)=-26

y^{^{''}} + 2 y^{^{'}} + 37 y = 0, y (0) = 2, y^{^{'}} (0) = - 26