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Form the differential equation of family...

Form the differential equation of family of lines concurrent at the origin.

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Equation of family of line concurrent at origin is given by y=mx
`therefore (dy)/(dx)=m`
Putting the value of m in (1), we get
`y=(dy)/(dx).x`
or `xdy-ydx=0`, which is required differential equation of order q. Here order is same as number of effective constants in the equation of family of curve.
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  13. Solve the differential equation x y(dy)/( dx)=(1+y^2)/(1+x^2)(1+x+x^2)

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