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

Lösung

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

y = c_{1} e^{x} + c_{2} e^{- 3 x} + e^{x} x

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 3 x} + e^{x} x

y = c_{1} e^{x} + c_{2} e^{- 3 x} + e^{x} x

y^{^{''}} + 2 y = sin (x)

y^{^{''}} + 2 y^{^{'}} + 2 y = e^{- x} (cos (x) + 1)

y^{^{''}} - 4 y^{^{'}} + 8 y = e^{x} cos (2 x)

y^{^{''}} + 2 y^{^{'}} + y = e^{- 2 t}, y (0) = 2, y^{^{'}} (0) = 1

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