(dx)/(dy)=(xy)/(1+y)

解答

\frac{d x}{d y} = \frac{x y}{1 + y}

x = \frac{e ^{1 + y + c_{1}}}{1 + y}

求解步骤

\frac{d x}{d y} = \frac{x y}{1 + y}

求解可分离方程:

x = \frac{e ^{1 + y + c_{1}}}{1 + y}

x = \frac{e ^{1 + y + c_{1}}}{1 + y}

y^{^{'}} - \frac{t ^{5}}{y} = 0

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

y^{^{'}} = y (\frac{a}{x ^{2}} + b x)

\frac{d y}{d t} = 0.48 - \frac{y}{240}

f (x) = f^{^{'}} (x) (4 x + 9)^{5}