(dy)/(dx)y=(2x+5)(x^3-x^8)(x^{-7})

Lösung

\frac{d y}{d x} y = (2 x + 5) (x^{3} - x^{8}) (x^{- 7})

y = \frac{- 4 x ^{6} - 6 x - 10 - 15 x ^{5} + 6 c _{1} x ^{3}}{3 x x}, y = - \frac{- 4 x ^{6} - 6 x - 10 - 15 x ^{5} + 6 c _{1} x ^{3}}{3 x x}

Schritte zur Lösung

\frac{d y}{d x} y = (2 x + 5) (x^{3} - x^{8}) (x^{- 7})

Solve separable ODE:

y = \frac{- 4 x ^{6} - 6 x - 10 - 15 x ^{5} + 6 c _{1} x ^{3}}{3 x x}, y = - \frac{- 4 x ^{6} - 6 x - 10 - 15 x ^{5} + 6 c _{1} x ^{3}}{3 x x}

y = \frac{- 4 x ^{6} - 6 x - 10 - 15 x ^{5} + 6 c _{1} x ^{3}}{3 x x}, y = - \frac{- 4 x ^{6} - 6 x - 10 - 15 x ^{5} + 6 c _{1} x ^{3}}{3 x x}

3 y^{4} - 1 + 12 x y^{3} y^{^{'}} = 0

\frac{d y}{d x} = \frac{2 x ^{2}}{y + 1}

y^{^{'}} - y = - 1

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

y^{^{'}} = \frac{4 x y}{x ^{2} + 1}