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

Lösung

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

y = c_{1} + c_{2} e^{- x} - e^{- x} x

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- x} - e^{- x} x

y = c_{1} + c_{2} e^{- x} - e^{- x} x

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

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

y^{^{''}} + 2 y + 1 = 0

y^{^{''}} + 2 y^{^{'}} - 15 = x^{2}

y^{^{''}} - y = e^{2 t}