(2xy-9x^2)+(2y+x^2+1)(dy)/(dx)=0

解

(2 x y - 9 x^{2}) + (2 y + x^{2} + 1) \frac{d y}{d x} = 0

y = \frac{- 1 - x ^{2} + ( 1 + x ^{2} ) ^{2} - 4 ( - 3 x ^{3} - c _{1} )}{2}, y = \frac{- 1 - x ^{2} - ( 1 + x ^{2} ) ^{2} - 4 ( - 3 x ^{3} - c _{1} )}{2}

解答ステップ

(2 x y - 9 x^{2}) + (2 y + x^{2} + 1) \frac{d y}{d x} = 0

完全 ODE を解く:

y = \frac{- 1 - x ^{2} + ( 1 + x ^{2} ) ^{2} - 4 ( - 3 x ^{3} - c _{1} )}{2}, y = \frac{- 1 - x ^{2} - ( 1 + x ^{2} ) ^{2} - 4 ( - 3 x ^{3} - c _{1} )}{2}

y = \frac{- 1 - x ^{2} + ( 1 + x ^{2} ) ^{2} - 4 ( - 3 x ^{3} - c _{1} )}{2}, y = \frac{- 1 - x ^{2} - ( 1 + x ^{2} ) ^{2} - 4 ( - 3 x ^{3} - c _{1} )}{2}