(x^2+9)dy=(2x-8xy)dx

解

(x^{2} + 9) d y = (2 x - 8 x y) d x

y = \frac{c _{1}}{4 ( x ^{8} + 36 x ^{6} + 486 x ^{4} + 2916 x ^{2} + 6561 )} + \frac{1}{4}

解答ステップ

(x^{2} + 9) d y = (2 x - 8 x y) d x

分離可能 ODE を解く:

y = \frac{c _{1}}{4 ( x ^{8} + 36 x ^{6} + 486 x ^{4} + 2916 x ^{2} + 6561 )} + \frac{1}{4}

y = \frac{c _{1}}{4 ( x ^{8} + 36 x ^{6} + 486 x ^{4} + 2916 x ^{2} + 6561 )} + \frac{1}{4}