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

Lösung

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}

Schritte zur Lösung

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

Solve separable ODE:

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}

2 x y^{^{'}} + x^{2} y = 0

y^{^{'}} = \frac{x + x y ^{2}}{4 x}

\frac{d y}{d x} = \frac{sin ( 5 x )}{y}

\frac{d}{d x} ((y) \cdot 10) + 5 y = 0

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