(x-7)^4y^'+5(x-7)^3y=x+7

解

(x - 7)^{4} y^{^{'}} + 5 (x - 7)^{3} y = x + 7

y = \frac{x ^{3}}{3 ( x ^{5} - 35 x ^{4} + 490 x ^{3} - 3430 x ^{2} + 12005 x - 16807 )} - \frac{49 x}{x ^{5} - 35 x ^{4} + 490 x ^{3} - 3430 x ^{2} + 12005 x - 16807} + \frac{c _{1}}{x ^{5} - 35 x ^{4} + 490 x ^{3} - 3430 x ^{2} + 12005 x - 16807}

解答ステップ

(x - 7)^{4} y^{'} (x) + 5 (x - 7)^{3} y = x + 7

線形 ODE を解く:

y = \frac{x ^{3}}{3 ( x ^{5} - 35 x ^{4} + 490 x ^{3} - 3430 x ^{2} + 12005 x - 16807 )} - \frac{49 x}{x ^{5} - 35 x ^{4} + 490 x ^{3} - 3430 x ^{2} + 12005 x - 16807} + \frac{c _{1}}{x ^{5} - 35 x ^{4} + 490 x ^{3} - 3430 x ^{2} + 12005 x - 16807}

y = \frac{x ^{3}}{3 ( x ^{5} - 35 x ^{4} + 490 x ^{3} - 3430 x ^{2} + 12005 x - 16807 )} - \frac{49 x}{x ^{5} - 35 x ^{4} + 490 x ^{3} - 3430 x ^{2} + 12005 x - 16807} + \frac{c _{1}}{x ^{5} - 35 x ^{4} + 490 x ^{3} - 3430 x ^{2} + 12005 x - 16807}