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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{3}{50} e^{x} sin (x) + \frac{2}{25} e^{x} cos (x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{3}{50} e^{x} sin (x) + \frac{2}{25} e^{x} cos (x)

y = c_{1} e^{- 2 x} + c_{2} x e^{- 2 x} + \frac{3}{50} e^{x} sin (x) + \frac{2}{25} e^{x} cos (x)

Graph

Beliebte Beispiele

y^{''}+4y^'+13y=5cos(2t)

y^{^{''}} + 4 y^{^{'}} + 13 y = 5 cos (2 t)

x^{''}-6x^'+10x=30t

x^{^{''}} - 6 x^{^{'}} + 10 x = 30 t

y^{''}-y^'-12y=(x+1)e^x

y^{^{''}} - y^{^{'}} - 12 y = (x + 1) e^{x}

y^{''}-14y^'+49y=35x+4

y^{^{''}} - 14 y^{^{'}} + 49 y = 35 x + 4

(d^2y)/(dt^2)+4y=sec^2(2t)

\frac{d ^{2} y}{d t ^{2}} + 4 y = sec^{2} (2 t)