y^'=(5x^2-1)/(5+6y)

解

y^{^{'}} = \frac{5 x ^{2} - 1}{5 + 6 y}

y = \frac{- 5 + - 4 ( - 5 x ^{3} + 3 x - c _{1} ) + 25}{6}, y = - \frac{- 4 ( - 5 x ^{3} + 3 x - c _{1} ) + 25 + 5}{6}

解答ステップ

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

分離可能 ODE を解く:

y = \frac{- 5 + - 4 ( - 5 x ^{3} + 3 x - c _{1} ) + 25}{6}, y = - \frac{- 4 ( - 5 x ^{3} + 3 x - c _{1} ) + 25 + 5}{6}

y = \frac{- 5 + - 4 ( - 5 x ^{3} + 3 x - c _{1} ) + 25}{6}, y = - \frac{- 4 ( - 5 x ^{3} + 3 x - c _{1} ) + 25 + 5}{6}