(1-y)(dy)/(dx)=x^2

解答

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

y = - \frac{- 6 + 36 + 12 ( - c _{1} - 2 x ^{3} )}{6}, y = - \frac{- 6 - 36 + 12 ( - c _{1} - 2 x ^{3} )}{6}

求解步骤

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

求解可分离方程:

y = - \frac{- 6 + 36 + 12 ( - c _{1} - 2 x ^{3} )}{6}, y = - \frac{- 6 - 36 + 12 ( - c _{1} - 2 x ^{3} )}{6}

y = - \frac{- 6 + 36 + 12 ( - c _{1} - 2 x ^{3} )}{6}, y = - \frac{- 6 - 36 + 12 ( - c _{1} - 2 x ^{3} )}{6}

\frac{d y}{d x} y = \frac{sin ( x )}{x ^{3}}

y^{^{'}} = \frac{ln ( x )}{x y}

\frac{d y}{d x} = - \frac{1}{sin ( y )}, y (- 3) = \frac{π}{2}

\frac{d y}{d x} (- y cot (x)) = \frac{sin ( 2 x )}{2}

y^{^{'}} = \frac{x ^{2} + 7 x + 3}{y ^{2}}, y (0) = 3