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Question Number 51710 by sinx last updated on 29/Dec/18

$$solvetheequation$$$$y={xy}^{\prime }+{\left(y^{\prime }\right)}^2$$

Answered by Abdulhafeez Abu qatada last updated on 30/Dec/18

$$$$$$$$$$y^{\prime }=y^{\prime }+{xy}^{″}+2y^{\prime }{y}^{″}$$$${xy}^{″}+2y^{\prime }{y}^{″}=0$$$$x+2y^{\prime }=0,y^{″}=0$$$$2y^{\prime }=-x$$$$y^{\prime }=-\frac{x}{2}$$$$y=\frac{-x^2}{4}+\mathrm{C}$$$$$$$$whichsatisfiesthat{y}^{″}=0$$

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