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

Find the general solution of dy/dx=x+y/x-y.

1. y/x = C - ≤ft( x2 + y2 )
2. x/y = C + ≤ft( x2 + y2 )
3. y/x = C + ≤ft( x2 + y2 )
4. y/x = C + ≤ft(x2 + y2 )

Answer

C. y/x = C + ≤ft( x2 + y2 )

Solution

With y=vx: v+xv'=1+v/1-v (1-v),dv/1+v2=dx/x v- 12 (1+v2)= x+c. Substituting back gives yx= (x2+y2)+C.

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