e^{x^3-y^2}+y/(x^2)y^'=0

解答

e^{x^{3} - y^{2}} + \frac{y}{x ^{2}} y^{^{'}} = 0

y = ln (- \frac{2}{3} e^{x^{3}} + c_{1}), y = - ln (- \frac{2}{3} e^{x^{3}} + c_{1})

求解步骤

e^{x^{3} - y^{2}} + \frac{y}{x ^{2}} y^{'} (x) = 0

求解可分离方程:

y = ln (- \frac{2}{3} e^{x^{3}} + c_{1}), y = - ln (- \frac{2}{3} e^{x^{3}} + c_{1})

y = ln (- \frac{2}{3} e^{x^{3}} + c_{1}), y = - ln (- \frac{2}{3} e^{x^{3}} + c_{1})

sec (y) d x + (csc^{2} (x)) d y = 0

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

14 y^{6} \frac{d y}{d x} = 8 x^{7}

7 x y \frac{d y}{d x} = 4, y > 0, x > 0

\frac{d y}{d x} = x y, y (- 1) = \frac{25}{16}