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The differential equation y=px+f(p), ………...

The differential equation `y=px+f(p)`, …………..(i)
where `p=(dy)/(dx)`,is known as Clairout's equation. To solve equation i) differentiate it with respect to x, which gives either
`(dp)/(dx)=0 rArr p =c`………….(ii)
or `x+f^(i)(p)=0`…………(iii)
The singular solution of the differential equation `y=mx + m-m^(3)`, where `m=(dy)/(dx)`, passes through the point.

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