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

解答

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

y = c_{1} + c_{2} e^{x} + c_{3} e^{2 x} - \frac{x ^{3}}{2} - \frac{9 x ^{2}}{4} - \frac{9 x}{4}

求解步骤

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

求解线性方程:

y = c_{1} + c_{2} e^{x} + c_{3} e^{2 x} - \frac{x ^{3}}{2} - \frac{9 x ^{2}}{4} - \frac{9 x}{4}

y = c_{1} + c_{2} e^{x} + c_{3} e^{2 x} - \frac{x ^{3}}{2} - \frac{9 x ^{2}}{4} - \frac{9 x}{4}

y^{^{''}} - 4 y^{^{'}} + 3 y = 3 + 3 x, y (0) = 1, y^{^{'}} (0) = 3

y^{^{'''}} - 3 y^{^{'}} - 2 y = e^{x} (x e^{x} + 1)

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = e^{x}

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

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