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Beliebt Rechnen >

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

Lösung

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{x s e c (x)}

Lösung

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + e^{x} cos (x) \cdot \int - e^{- x + x s e c (x)} sin (x) d x + e^{x} sin (x) \cdot \int e^{- x + x s e c (x)} cos (x) d x

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) + 2 y = e^{x s e c (x)}

Solve linear ODE:

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + e^{x} cos (x) \cdot \int - e^{- x + x s e c (x)} sin (x) d x + e^{x} sin (x) \cdot \int e^{- x + x s e c (x)} cos (x) d x

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + e^{x} cos (x) \cdot \int - e^{- x + x s e c (x)} sin (x) d x + e^{x} sin (x) \cdot \int e^{- x + x s e c (x)} cos (x) d x

Beliebte Beispiele

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

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

y^{''}-4y^'+4y=3t^2+4+e^{2t}+tsin(2t)

y^{^{''}} - 4 y^{^{'}} + 4 y = 3 t^{2} + 4 + e^{2 t} + t sin (2 t)

y^{''}-5y^'-6y=5xe^{-x}

y^{^{''}} - 5 y^{^{'}} - 6 y = 5 x e^{- x}

x^{''}+x=8cos(5t)

x^{^{''}} + x = 8 cos (5 t)

y^{^{'''}} + y^{^{'}} = 2