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:

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