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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}-3y^'-4y=xe^x+2cos(x)-sin(x)

y^{^{''}} - 3 y^{^{'}} - 4 y = x e^{x} + 2 cos (x) - sin (x)

D(D-1)^3y=(x^2+2x)e^x

D (D - 1)^{3} y = (x^{2} + 2 x) e^{x}

y^{''}+4y=(cos(2x))/2

y^{^{''}} + 4 y = \frac{cos ( 2 x )}{2}

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

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

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

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