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Question

If the solution of the differential equation x(d3ydx3)+d2ydx2+2x(dydx)y+1=0 is a straight line of the form y=mx+c, where m,c are real constants, then the number of such possible lines is 
  1. 1
  2. 2
  3. 3
  4. infinite 


Solution

The correct option is A 1
Given that the equation of line y=mx+c
y=m,  y′′=0,  y′′′=0
x×0+0+2xmmxc+1=0mxc+1=0m=0,  c=1

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