y^{''}-5y^'+6y=x^3+2x^2+5x+2

解

y^{^{''}} - 5 y^{^{'}} + 6 y = x^{3} + 2 x^{2} + 5 x + 2

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{3}}{6} + \frac{3 x ^{2}}{4} + \frac{23 x}{12} + \frac{121}{72}

解答ステップ

y^{''} (x) - 5 y^{'} (x) + 6 y = x^{3} + 2 x^{2} + 5 x + 2

線形 ODE を解く:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{3}}{6} + \frac{3 x ^{2}}{4} + \frac{23 x}{12} + \frac{121}{72}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{3}}{6} + \frac{3 x ^{2}}{4} + \frac{23 x}{12} + \frac{121}{72}