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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

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

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 36 y = 4

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

y^{^{''}} + 6 y + 34 = 0, y (0) = 1, y^{^{'}} (0) = 7

y^{^{''}} + 25 y = 2 cos (5.1 t), y (0) = 1, y^{^{'}} (0) = 1