(1+x^2)y^'-xy=xy^2

解

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

y = \frac{e ^{c_{1}} ( 1 + x ^{2} ) ^{\frac{1}{2}} + e ^{2 c_{1}} + e ^{2 c_{1}} x ^{2}}{1 - e ^{2 c_{1}} x ^{2} - e ^{2 c_{1}}}

解答ステップ

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

分離可能 ODE を解く:

y = \frac{e ^{c_{1}} ( 1 + x ^{2} ) ^{\frac{1}{2}} + e ^{2 c_{1}} + e ^{2 c_{1}} x ^{2}}{1 - e ^{2 c_{1}} x ^{2} - e ^{2 c_{1}}}

y = \frac{e ^{c_{1}} ( 1 + x ^{2} ) ^{\frac{1}{2}} + e ^{2 c_{1}} + e ^{2 c_{1}} x ^{2}}{1 - e ^{2 c_{1}} x ^{2} - e ^{2 c_{1}}}