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Beliebt Rechnen >

y^{''}+4y^'+5y=e^{-2x}sin(x)

Lösung

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{- 2 x} sin (x)

Lösung

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

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 5 y = e^{- 2 x} sin (x)

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+8y^'+20y=100x^2-26xe^x

y^{^{''}} + 8 y^{^{'}} + 20 y = 100 x^{2} - 26 x e^{x}

y^{''}+4y^'+4y=xe^{2x}

y^{^{''}} + 4 y^{^{'}} + 4 y = x e^{2 x}

2y^{''}+y^'+4y=x+1

2 y^{^{''}} + y^{^{'}} + 4 y = x + 1

y^{''}-y^'-6y=2x

y^{^{''}} - y^{^{'}} - 6 y = 2 x

y^{''}-y^'-6y=5-6^x,y(0)=2,y^'(0)=4

y^{^{''}} - y^{^{'}} - 6 y = 5 - 6^{x}, y (0) = 2, y^{^{'}} (0) = 4