4x+5yy^'=3x^2+4y^3y^'

解

4 x + 5 y y^{^{'}} = 3 x^{2} + 4 y^{3} y^{^{'}}

y = - \frac{- 5 + 25 + 8 ( - c _{1} + 4 x ^{2} - 2 x ^{3} )}{4}, y = - - \frac{- 5 + 25 + 8 ( - c _{1} + 4 x ^{2} - 2 x ^{3} )}{4}, y = \frac{5 + 25 + 8 ( - c _{1} + 4 x ^{2} - 2 x ^{3} )}{2}, y = - \frac{5 + 25 + 8 ( - c _{1} + 4 x ^{2} - 2 x ^{3} )}{2}

解答ステップ

4 x + 5 y y^{'} (x) = 3 x^{2} + 4 y^{3} y^{'} (x)

分離可能 ODE を解く:

y = - \frac{- 5 + 25 + 8 ( - c _{1} + 4 x ^{2} - 2 x ^{3} )}{4}, y = - - \frac{- 5 + 25 + 8 ( - c _{1} + 4 x ^{2} - 2 x ^{3} )}{4}, y = \frac{5 + 25 + 8 ( - c _{1} + 4 x ^{2} - 2 x ^{3} )}{2}, y = - \frac{5 + 25 + 8 ( - c _{1} + 4 x ^{2} - 2 x ^{3} )}{2}

y = - \frac{- 5 + 25 + 8 ( - c _{1} + 4 x ^{2} - 2 x ^{3} )}{4}, y = - - \frac{- 5 + 25 + 8 ( - c _{1} + 4 x ^{2} - 2 x ^{3} )}{4}, y = \frac{5 + 25 + 8 ( - c _{1} + 4 x ^{2} - 2 x ^{3} )}{2}, y = - \frac{5 + 25 + 8 ( - c _{1} + 4 x ^{2} - 2 x ^{3} )}{2}