Engineering Board Exam Reviewer · Bernoulli and Reducible Equations · medium

Find the general solution of dy/dx+y/x=xy2 for x>0.

1. y = 1C x + x2
2. y = 1C x - x2
3. y = 1C x - x33
4. y = C x - x2

Answer

B. y = 1C x - x2

Solution

Bernoulli with n=2. Let v=y-1: v'=-y-2y'=-x+ vx, i.e. v'- vx=-x. The integrating factor is 1x: d/dx≤ft( vx )=-1 v=-x2+Cx. So y=1/Cx-x2.

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1. Find the general solution of dy/dx+y=xy2.
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3. Find the general solution of dy/dx+y/x=xy3 for x>0.
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