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

解

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}

解答ステップ

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

代用

\frac{d y}{d x}

と

y^{'} (x)

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

分離する

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}