(x^2y+2y)y^'=2xy^2+2x

解答

(x^{2} y + 2 y) y^{^{'}} = 2 x y^{2} + 2 x

y = e^{2 c_{1}} x^{4} + 4 e^{2 c_{1}} x^{2} + 4 e^{2 c_{1}} - 1, y = - e^{2 c_{1}} x^{4} + 4 e^{2 c_{1}} x^{2} + 4 e^{2 c_{1}} - 1

求解步骤

(x^{2} y + 2 y) y^{'} (x) = 2 x y^{2} + 2 x

求解可分离方程:

y = e^{2 c_{1}} x^{4} + 4 e^{2 c_{1}} x^{2} + 4 e^{2 c_{1}} - 1, y = - e^{2 c_{1}} x^{4} + 4 e^{2 c_{1}} x^{2} + 4 e^{2 c_{1}} - 1

y = e^{2 c_{1}} x^{4} + 4 e^{2 c_{1}} x^{2} + 4 e^{2 c_{1}} - 1, y = - e^{2 c_{1}} x^{4} + 4 e^{2 c_{1}} x^{2} + 4 e^{2 c_{1}} - 1

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

sec^{2} (x) y^{^{'}} = - csc (y)

y^{^{'}} = e^{x - y}, y (0) = 1

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

y^{^{'}} = 7 y^{- 2}, y (0) = 3