Engineering Board Exam Reviewer · Bernoulli and Reducible Equations · medium

Find the general solution of dy/dx+y=xy2.

1. y = 1C ex + x + 1
2. y = 1C ex + x - 1
3. y = C ex + x + 1
4. y = 1C e- x + x + 1

Answer

A. y = 1C ex + x + 1

Solution

Bernoulli with n=2. Let v=y-1: v'=-y-2y'=-x+v, i.e. v'-v=-x. The integrating factor is e-x: d/dx≤ft(ve-x )=-xe-x ve-x=xe-x+e-x+C. So v=x+1+Cex and y= 1x+1+Cex.

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1. Which substitution reduces the Bernoulli equation dy/dx+P(x)y=Q(x)yn to a linear equation?
2. Find the general solution of dy/dx+y/x=xy3 for x>0.
3. Find the general solution of dy/dx=(y-x)2+1.
4. Find the general solution of dy/dx=(x+y)2.
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