y^{'''}=x^4

解

y^{^{'''}} = x^{4}

y = \frac{x ^{7}}{210} + \frac{c _{1} x ^{2}}{2} + c_{2} x + c_{3}

解答ステップ

y^{'''} (x) = x^{4}

解く

y^{'''} (x) = x^{4} : y^{''} (x) = \frac{x ^{5}}{5} + c_{1}

解く

y^{''} (x) = \frac{x ^{5}}{5} + c_{1} : y^{'} (x) = \frac{x ^{6}}{30} + c_{1} x + c_{2}

解く

y^{'} (x) = \frac{x ^{6}}{30} + c_{1} x + c_{2} : y = \frac{x ^{7}}{210} + \frac{c _{1} x ^{2}}{2} + c_{2} x + c_{3}

y = \frac{x ^{7}}{210} + \frac{c _{1} x ^{2}}{2} + c_{2} x + c_{3}