Engineering Board Exam Reviewer · Bernoulli and Reducible Equations · hard

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

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

Answer

C. 1y2 = x2 ≤ft(C - 2 x )

Solution

Bernoulli with n=3. Let v=y-2: v'=-2y-3y'=-2x+2v/x, i.e. v'-2/xv=-2x. The integrating factor is x-2: d/dx≤ft(vx-2 )=- 2x vx-2=-2 x+C. So 1y2=x2(C-2 x).

More Bernoulli and Reducible Equations questions

1. Find the general solution of dy/dx=(y-x)2+1.
2. Find the general solution of dy/dx=(x+y)2.
3. Find the general solution of dy/dx+y/x=xy2 for x>0.
4. Find the general solution of dy/dx+y=xy2.
5. Which substitution reduces the Bernoulli equation dy/dx+P(x)y=Q(x)yn to a linear equation?

All Bernoulli and Reducible Equations questions