y^{''}-y-x=0

解答

y^{^{''}} - y - x = 0

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

求解步骤

y^{''} (x) - y - x = 0

求解线性方程:

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

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

(D^{2} + 2) y = e^{x + 2}

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

y^{^{''}} + 8 y^{^{'}} + 17 y = 2 e^{- 4 t} cos (t)

y^{^{''}} - 8 y^{^{'}} + 20 y = 100 x^{2} + 26 x e^{x}

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} 4 + 8 y = 8 x^{2}