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Beliebt Rechnen >

y^{''}-3y^'-10y=-4e^{4t},y(0)=0,y^'(0)=0

Lösung

y^{^{''}} - 3 y^{^{'}} - 10 y = - 4 e^{4 t}, y (0) = 0, y^{^{'}} (0) = 0

Lösung

y = (\frac{2}{21} - \frac{2}{3}) e^{5 t} - \frac{2}{21} e^{- 2 t} + \frac{2}{3} e^{4 t}

Schritte zur Lösung

y^{''} (t) - 3 y^{'} (t) - 10 y = - 4 e^{4 t}

Solve linear ODE:

y = (\frac{2}{21} - \frac{2}{3}) e^{5 t} - \frac{2}{21} e^{- 2 t} + \frac{2}{3} e^{4 t}

y = (\frac{2}{21} - \frac{2}{3}) e^{5 t} - \frac{2}{21} e^{- 2 t} + \frac{2}{3} e^{4 t}

Graph

Beliebte Beispiele

integral of 12e^{4x}

\int 12 e^{4 x} d x

laplacetransform 10t^3e^{-2t}

l a pl a ce t r an s f or m 10 t^{3} e^{- 2 t}

y^{''}-y^'=6xe^x

y^{^{''}} - y^{^{'}} = 6 x e^{x}

limit as x approaches 1 of (1-x)/(\sqrt[3]{8x^3-8)}

x \to 1 lim (\frac{1 - x}{3 8 x ^{3} - 8})

derivative of-12x^2

\frac{d}{d x} (- 12 x^{2})