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Beliebt Rechnen >

y^{''}-2y^'+y=10e^{-2x}cos(x)

Lösung

y^{^{''}} - 2 y^{^{'}} + y = 10 e^{- 2 x} cos (x)

Lösung

y = c_{1} e^{x} + c_{2} x e^{x} - \frac{3}{5} e^{- 2 x} sin (x) + \frac{4}{5} e^{- 2 x} cos (x)

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) + y = 10 e^{- 2 x} cos (x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} - \frac{3}{5} e^{- 2 x} sin (x) + \frac{4}{5} e^{- 2 x} cos (x)

y = c_{1} e^{x} + c_{2} x e^{x} - \frac{3}{5} e^{- 2 x} sin (x) + \frac{4}{5} e^{- 2 x} cos (x)

Graph

Beliebte Beispiele

y^{''}-y=sinh(x)

y^{^{''}} - y = sinh (x)

4y^{''}-y=e^{x/2}+9

4 y^{^{''}} - y = e^{\frac{x}{2}} + 9

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

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

y^{''}+9y=9sec(3x)

y^{^{''}} + 9 y = 9 sec (3 x)

5y^{''}-10y^'+5y=e^xln(x)

5 y^{^{''}} - 10 y^{^{'}} + 5 y = e^{x} ln (x)