Let $$y=y(x)$$ be the solution curve of the differential equation $$y2$$−$$xdydx=1$$, satisfying $$y(0)$$ $$=$$ $$1$$. This curve intersects the $$x-axis$$ at a point whose abscissa is:

Question

Let $$y=y(x)$$ be the solution curve of the differential equation $$y2$$−$$xdydx=1$$, satisfying $$y(0)$$ $$=$$ $$1$$. This curve intersects the $$x-axis$$ at a point whose abscissa is:

Infinity Learn · Accepted Answer

We have $$dxdy+x=y2I$$.F. $$=e$$∫$$1dy=ey$$∴Solution is x.$$ey=$$∫$$y2$$.ey.dy       $$=y2$$.ey−∫$$2y$$.ey.dy      $$=y2ey$$−$$2y$$.ey−$$ey+c$$∴x.$$ey=y2ey$$−$$2yey+2ey+C$$⇒$$x=y2$$−$$2y+2+c$$.e−yGiven $$x=0$$,   $$y=1$$⇒$$0=1$$−$$2+2+ce$$⇒$$c=$$−eNow. curve cuts $$x-axis$$ ⇒$$y=0$$⇒$$x=0$$−$$0+2+$$−ee−$$0$$⇒$$x=2$$−e

Let y=y(x) be the solution curve of the differential equation $(y^{2} - x) \frac{d y}{d x} = 1$ , satisfying y(0) = 1. This curve intersects the x-axis at a point whose abscissa is:

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Let y=y(x) be the solution curve of the differential equation y2−xdydx=1, satisfying y(0) = 1. This curve intersects the x-axis at a point whose abscissa is:

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Let y=y(x) be the solution curve of the differential equation $(y^{2} - x) \frac{d y}{d x} = 1$ , satisfying y(0) = 1. This curve intersects the x-axis at a point whose abscissa is: