y^{''}-y^'-6y=3x-1

解答

y^{^{''}} - y^{^{'}} - 6 y = 3 x - 1

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{x}{2} + \frac{1}{4}

求解步骤

y^{''} (x) - y^{'} (x) - 6 y = 3 x - 1

求解线性方程:

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{x}{2} + \frac{1}{4}

y = c_{1} e^{3 x} + c_{2} e^{- 2 x} - \frac{x}{2} + \frac{1}{4}

(d^{2} + 3 d + 2) \cdot y = e^{e^{x}}

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

(d^{2} + d - 6) y = e^{2} x \cdot sin^{3} (x)

y^{^{''}} + y^{^{'}} - 6 y = 6 x^{2} - 2 x - 2

(d^{2} - 4 d + 4) \cdot y = x^{3}