y^{''}+8y=5x+2e^{-x}

Lösung

y^{^{''}} + 8 y = 5 x + 2 e^{- x}

y = c_{1} cos (2^{1 + \frac{1}{2}} x) + c_{2} sin (2^{1 + \frac{1}{2}} x) + \frac{5 x}{8} + \frac{2}{9} e^{- x}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} cos (2^{1 + \frac{1}{2}} x) + c_{2} sin (2^{1 + \frac{1}{2}} x) + \frac{5 x}{8} + \frac{2}{9} e^{- x}

y = c_{1} cos (2^{1 + \frac{1}{2}} x) + c_{2} sin (2^{1 + \frac{1}{2}} x) + \frac{5 x}{8} + \frac{2}{9} e^{- x}

y^{^{''}} + a \frac{d y}{d t} + b y = c sin (g t)

x^{^{''}} + 4 x^{^{'}} + 13 x = 5 cos (2 t)

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

y^{^{''}} - 3 y^{^{'}} + 2 y = 2 e^{- 3 t}, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - y^{^{'}} = x e^{x}, y (0) = 2, y^{^{'}} (0) = 1