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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{- x} + c_{2} x e^{- x} - \frac{1}{2} cos (x) + \frac{8}{25} sin (2 x) - \frac{6}{25} cos (2 x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} x e^{- x} - \frac{1}{2} cos (x) + \frac{8}{25} sin (2 x) - \frac{6}{25} cos (2 x)

y = c_{1} e^{- x} + c_{2} x e^{- x} - \frac{1}{2} cos (x) + \frac{8}{25} sin (2 x) - \frac{6}{25} cos (2 x)

Graph

Beliebte Beispiele

(d^{2} - 1) y = x^{2}

y^{'''}-9y^{''}+27y^'-27y=4e^{3x}

y^{^{'''}} - 9 y^{^{''}} + 27 y^{^{'}} - 27 y = 4 e^{3 x}

(D^3-7D-6)y=e^{2x}(1+x)

(D^{3} - 7 D - 6) y = e^{2 x} (1 + x)

y^{''}-2y^'-3y=8e^{5x}

y^{^{''}} - 2 y^{^{'}} - 3 y = 8 e^{5 x}

y^{''}+8y=5x+2e^{-x}

y^{^{''}} + 8 y = 5 x + 2 e^{- x}