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

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

x \to \infty lim (\frac{0}{1})

\frac{\partial}{\partial x} (\frac{( 9 y + 7 z )}{x + u})

\int \frac{3 r ^{2}}{r + 5} d r

s l o p e in t erce pt (3, 5), (1, - 7)

x \to 0 lim (\frac{( 2 + x ^{3} ) - 8}{x})