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

Find the general solution of dy/dx=x2+y2/2xy.

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

Answer

D. y2 = C x + x2

Solution

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

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