Engineering Board Exam Reviewer · Bernoulli and Reducible Equations · medium

Find the general solution of dy/dx=(x+y)2.

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

Answer

D. y = - x + ≤ft(C + x )

Solution

Let v=x+y: dv/dx=1+dy/dx=1+v2. Then dv/1+v2=dx v=x+C v= (x+C). So y= (x+C)-x.

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