y^'=(x-3)(y+1)^{(2/3)}

解答

y^{^{'}} = (x - 3) (y + 1)^{(\frac{2}{3})}

y = - x^{3} + \frac{x ^{6}}{216} - \frac{x ^{5}}{12} + \frac{c _{1} x ^{4}}{36} + \frac{x ^{4}}{2} + \frac{- c _{1} x ^{3} - c _{1}^{2} x}{3} + \frac{c _{1}^{2} x ^{2}}{18} + c_{1} x^{2} + \frac{c _{1}^{3}}{27} - 1

求解步骤

y^{'} (x) = (x - 3) (y + 1)^{(\frac{2}{3})}

求解可分离方程:

y = - x^{3} + \frac{x ^{6}}{216} - \frac{x ^{5}}{12} + \frac{c _{1} x ^{4}}{36} + \frac{x ^{4}}{2} + \frac{- c _{1} x ^{3} - c _{1}^{2} x}{3} + \frac{c _{1}^{2} x ^{2}}{18} + c_{1} x^{2} + \frac{c _{1}^{3}}{27} - 1

y = - x^{3} + \frac{x ^{6}}{216} - \frac{x ^{5}}{12} + \frac{c _{1} x ^{4}}{36} + \frac{x ^{4}}{2} + \frac{- c _{1} x ^{3} - c _{1}^{2} x}{3} + \frac{c _{1}^{2} x ^{2}}{18} + c_{1} x^{2} + \frac{c _{1}^{3}}{27} - 1

x \to 2 + lim (e^{\frac{3}{2 - x}})

\frac{d}{d x} (\frac{x ^{3} + y ^{3}}{x ^{2} + y ^{2}})

\int 23

\int \frac{x + 2}{x ^{2} ( x ^{2} + 1 )} d x

n = 1 \sum \infty \frac{1}{( 2 n - 1 ) 2 n}