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Beliebt Rechnen >

y^{''}+2y^'+2y=e^xcos(x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+40y^'+625y=100cos(10t)

y^{^{''}} + 40 y^{^{'}} + 625 y = 100 cos (10 t)

2y^{''}-y^'-2y=2e^{-t}

2 y^{^{''}} - y^{^{'}} - 2 y = 2 e^{- t}

y^{''}+4y=20e^t,y(0)=0,y^'(0)=2

y^{^{''}} + 4 y = 20 e^{t}, y (0) = 0, y^{^{'}} (0) = 2

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

y^{''}-15y^'+54y=39+54x

y^{^{''}} - 15 y^{^{'}} + 54 y = 39 + 54 x