y^{''}+7y^'=cos(2x)+8e^{-5x}

Lösung

y^{^{''}} + 7 y^{^{'}} = cos (2 x) + 8 e^{- 5 x}

y = c_{1} + c_{2} e^{- 7 x} + \frac{7}{106} sin (2 x) - \frac{1}{53} cos (2 x) - \frac{4}{5} e^{- 5 x}

Schritte zur Lösung

y^{''} (x) + 7 y^{'} (x) = cos (2 x) + 8 e^{- 5 x}

Solve linear ODE:

y = c_{1} + c_{2} e^{- 7 x} + \frac{7}{106} sin (2 x) - \frac{1}{53} cos (2 x) - \frac{4}{5} e^{- 5 x}

y = c_{1} + c_{2} e^{- 7 x} + \frac{7}{106} sin (2 x) - \frac{1}{53} cos (2 x) - \frac{4}{5} e^{- 5 x}

y^{^{''}} + 3 y^{^{'}} - 4 y = 2, y^{^{'}} (0) = 0, y (0) = 0

y^{^{''}} + 3 y^{^{'}} - 4 y = x^{2} e^{x}

y^{^{''}} - y^{^{'}} - 6 y = e^{- x} + 12 x

5 y^{^{''}} - 15 y = 40 e^{x}

y^{^{''}} + 6 y^{^{'}} + 10 y = e^{- 3 t}, y (0) = 4, y^{^{'}} (0) = 5