y^'=(y^2)/(x^3),y(2)=4

解答

y^{^{'}} = \frac{y ^{2}}{x ^{3}}, y (2) = 4

y = \frac{8 x ^{2}}{4 + x ^{2}}

求解步骤

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

求解可分离方程:

y = \frac{8 x ^{2}}{4 + x ^{2}}

y = \frac{8 x ^{2}}{4 + x ^{2}}

x y y^{^{'}} = (x + 1) (y + 1)

(3 y^{2} - 4 x^{- 1} y) d x + (3 x y - 4) d y = 0

x^{^{'}} = \frac{x ^{2}}{2}

y^{^{'}} = \frac{t}{y}, y (0) = 1

y^{^{'}} - 10 x y = 0