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

Lösung

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

y = - \frac{c _{1} x}{4} - \frac{c _{1}^{2}}{16}, y = \frac{c _{1} x}{2} - \frac{c _{1}^{2}}{4}

Schritte zur Lösung

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

Ersetze

\frac{d y}{d x}

mit

y^{'} (x)

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

Isoliere

y^{'} (x) : y^{'} (x) = - \frac{- x + x ^{2} - 4 y}{2}, y^{'} (x) = - \frac{- x - x ^{2} - 4 y}{2}

y^{'} (x) = - \frac{- x + x ^{2} - 4 y}{2} : y = - \frac{c _{1} x}{4} - \frac{c _{1}^{2}}{16}

y^{'} (x) = - \frac{- x - x ^{2} - 4 y}{2} : y = \frac{c _{1} x}{2} - \frac{c _{1}^{2}}{4}

y = - \frac{c _{1} x}{4} - \frac{c _{1}^{2}}{16}, y = \frac{c _{1} x}{2} - \frac{c _{1}^{2}}{4}

a re a y = 5 x^{2}, y^{2} = \frac{1}{5} x

\frac{d y}{d x} = x^{6} y

x \to 100 lim (8 x)

d er i v a t i v e \frac{1}{4 x ^{\frac{3}{2}}}

\frac{d}{d x} ((x + 3)^{4})