y^{''}-5y^'=2x^3-4x^2-x+6

解

y^{^{''}} - 5 y^{^{'}} = 2 x^{3} - 4 x^{2} - x + 6

y = c_{1} e^{5 x} + c_{2} - \frac{x ^{4}}{10} + \frac{14 x ^{3}}{75} + \frac{53 x ^{2}}{250} - \frac{697 x}{625}

解答ステップ

y^{''} (x) - 5 y^{'} (x) = 2 x^{3} - 4 x^{2} - x + 6

線形 ODE を解く:

y = c_{1} e^{5 x} + c_{2} - \frac{x ^{4}}{10} + \frac{14 x ^{3}}{75} + \frac{53 x ^{2}}{250} - \frac{697 x}{625}

y = c_{1} e^{5 x} + c_{2} - \frac{x ^{4}}{10} + \frac{14 x ^{3}}{75} + \frac{53 x ^{2}}{250} - \frac{697 x}{625}