Engineering Board Exam Reviewer · Homogeneous First-Order Equations · medium

Find the general solution of (x2-y2),dx+2xy,dy=0.

  1. x2 + y2 = C x
  2. x2 + y2 = C
  3. x2 - y2 = C x
  4. x2 + y2 = C x2

Answer

A. x2 + y2 = C x

Solution

Then dy/dx=y2-x2/2xy. With y=vx: xv'=-1-v2/2v 2v,dv/1+v2=-dx/x (1+v2)=- x+c. So x(1+v2)=C, i.e. x2+y2=Cx.

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