Engineering Board Exam Reviewer · Bernoulli and Reducible Equations · medium

Find the general solution of dy/dx=(y-x)2+1.

1. y = x - 1/C + x
2. y = x + 1/C + x
3. y = x - 1C + x2
4. y = - C

Answer

A. y = x - 1/C + x

Solution

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

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