(dy)/(dx)=-((y^2)/(1+y^2)e^{(-x)})

解答

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

y = \frac{c _{1} e ^{x} + 1 + ( - c _{1} e ^{x} - 1 ) ^{2} + 4 e ^{2 x}}{2 e ^{x}}, y = \frac{c _{1} e ^{x} + 1 - ( - c _{1} e ^{x} - 1 ) ^{2} + 4 e ^{2 x}}{2 e ^{x}}

求解步骤

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

求解可分离方程:

y = \frac{c _{1} e ^{x} + 1 + ( - c _{1} e ^{x} - 1 ) ^{2} + 4 e ^{2 x}}{2 e ^{x}}, y = \frac{c _{1} e ^{x} + 1 - ( - c _{1} e ^{x} - 1 ) ^{2} + 4 e ^{2 x}}{2 e ^{x}}

y = \frac{c _{1} e ^{x} + 1 + ( - c _{1} e ^{x} - 1 ) ^{2} + 4 e ^{2 x}}{2 e ^{x}}, y = \frac{c _{1} e ^{x} + 1 - ( - c _{1} e ^{x} - 1 ) ^{2} + 4 e ^{2 x}}{2 e ^{x}}

x \to 0 lim (\frac{1}{8} + x - (\frac{1}{8}))

\int (5 x^{2} + 3 x - 10) d x

\int \frac{18 x ^{2}}{x ^{4} - 41 x ^{2} + 400} d x

\frac{d}{d x} (4 x - x^{2} - 3)

y \to 15 lim (y + 3)