y^{''}-y=4e^{-x}

Lösung

y^{^{''}} - y = 4 e^{- x}

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

Schritte zur Lösung

y^{''} (x) - y = 4 e^{- x}

Solve linear ODE:

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

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

y^{^{''}} + 8 y + 15 = - 18 e^{- 2 t}, y (0) = - 6, y^{^{'}} (0) = 10

y^{^{''}} - 6 y^{^{'}} + 25 y = t^{2} + 2

y^{^{''}} + 2 y^{^{'}} + 5 y = e^{- t} cos (2 t)

y^{^{''}} + y = 5 e^{- 2 x}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 9 y^{^{'}} + 18 y = 2050 e^{(2 t)} cos (10 t)