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Beliebt Rechnen >

y^{''}+4y^'=2e^{-t},y(0)=2,y^'(0)=2

Lösung

y^{^{''}} + 4 y^{^{'}} = 2 e^{- t}, y (0) = 2, y^{^{'}} (0) = 2

Lösung

y = \frac{1}{3} + \frac{8}{3} - \frac{1}{3} e^{- 4 t} - \frac{2}{3} e^{- t}

Schritte zur Lösung

y^{''} (t) + 4 y^{'} (t) = 2 e^{- t}

Solve linear ODE:

y = \frac{1}{3} + \frac{8}{3} - \frac{1}{3} e^{- 4 t} - \frac{2}{3} e^{- t}

y = \frac{1}{3} + \frac{8}{3} - \frac{1}{3} e^{- 4 t} - \frac{2}{3} e^{- t}

Graph

Beliebte Beispiele

(D^2-2D+1)y=4x^2e^x

(D^{2} - 2 D + 1) y = 4 x^{2} e^{x}

x^{''}+4x^'+3x=4e^{-2t},x(0)=0,x^'(0)=0

x^{^{''}} + 4 x^{^{'}} + 3 x = 4 e^{- 2 t}, x (0) = 0, x^{^{'}} (0) = 0

y^{''}-4y^'=sin^2(x)

y^{^{''}} - 4 y^{^{'}} = sin^{2} (x)

y^{''}-4y^'+5y=5x^2+2x

y^{^{''}} - 4 y^{^{'}} + 5 y = 5 x^{2} + 2 x

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

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