(xy^')/(y-2)=y^2-y

Lösung

\frac{x y ^{^{'}}}{y - 2} = y^{2} - y

y = \frac{x ^{2} - c _{1}^{2} + c _{1} - x ^{2} + c _{1}^{2}}{x ^{2} - c _{1}^{2}}, y = \frac{x ^{2} - c _{1}^{2} - c _{1} - x ^{2} + c _{1}^{2}}{x ^{2} - c _{1}^{2}}

Schritte zur Lösung

\frac{x y ^{'} ( x )}{y - 2} = y^{2} - y

Solve linear ODE:

y = \frac{x ^{2} - c _{1}^{2} + c _{1} - x ^{2} + c _{1}^{2}}{x ^{2} - c _{1}^{2}}, y = \frac{x ^{2} - c _{1}^{2} - c _{1} - x ^{2} + c _{1}^{2}}{x ^{2} - c _{1}^{2}}

y = \frac{x ^{2} - c _{1}^{2} + c _{1} - x ^{2} + c _{1}^{2}}{x ^{2} - c _{1}^{2}}, y = \frac{x ^{2} - c _{1}^{2} - c _{1} - x ^{2} + c _{1}^{2}}{x ^{2} - c _{1}^{2}}

t an g e n t f (x) = \frac{- 6 x}{x ^{2} + 1}, (1, - 3)

a re a y = - x^{2} + 16, y = - \frac{1}{4} x - 1, 4 (y + 2.3) = 2.3 x

\int \frac{22 x ^{2}}{x ^{4} - 61 x ^{2} + 900} d x

x \to 7 lim (\frac{7 - x}{7 - x})

x \to 6 lim (- 110)