(x^2y+y)y^'=2xy^2+6x

解答

(x^{2} y + y) y^{^{'}} = 2 x y^{2} + 6 x

y = e^{2 c_{1}} x^{4} + 2 e^{2 c_{1}} x^{2} + e^{2 c_{1}} - 3, y = - e^{2 c_{1}} x^{4} + 2 e^{2 c_{1}} x^{2} + e^{2 c_{1}} - 3

求解步骤

(x^{2} y + y) y^{'} (x) = 2 x y^{2} + 6 x

求解可分离方程:

y = e^{2 c_{1}} x^{4} + 2 e^{2 c_{1}} x^{2} + e^{2 c_{1}} - 3, y = - e^{2 c_{1}} x^{4} + 2 e^{2 c_{1}} x^{2} + e^{2 c_{1}} - 3

y = e^{2 c_{1}} x^{4} + 2 e^{2 c_{1}} x^{2} + e^{2 c_{1}} - 3, y = - e^{2 c_{1}} x^{4} + 2 e^{2 c_{1}} x^{2} + e^{2 c_{1}} - 3

n = 1 \sum \infty arctan (n)

x \to 0 + lim ((4 x)^{\frac{4}{x}})

\int \frac{1}{y ^{2} + 2 y} d y

x \to \infty lim (3 x)

x \to 1 lim (3 1 - x)