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Beliebt Rechnen >

y^{''}+4y^'+8y=x+e^x

Lösung

y^{^{''}} + 4 y^{^{'}} + 8 y = x + e^{x}

Lösung

y = e^{- 2 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{x}{8} - \frac{1}{16} + \frac{1}{13} e^{x}

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 8 y = x + e^{x}

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{x}{8} - \frac{1}{16} + \frac{1}{13} e^{x}

y = e^{- 2 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{x}{8} - \frac{1}{16} + \frac{1}{13} e^{x}

Graph

Beliebte Beispiele

y^{''}+4y=2e^{2t}+4cos(3t)

y^{^{''}} + 4 y = 2 e^{2 t} + 4 cos (3 t)

y^{''}-16y^'=2e^{4x}

y^{^{''}} - 16 y^{^{'}} = 2 e^{4 x}

y^{'''}+4y^'=t^2+2t

y^{^{'''}} + 4 y^{^{'}} = t^{2} + 2 t

y^{''}-y=sin(t),y(0)=1,y^'(0)=1

y^{^{''}} - y = sin (t), y (0) = 1, y^{^{'}} (0) = 1

4y^{''}+8y^'+5y=e^{-x}sec(x/2)

4 y^{^{''}} + 8 y^{^{'}} + 5 y = e^{- x} sec (\frac{x}{2})