Engineering Board Exam Reviewer · Bernoulli and Reducible Equations · easy

Which substitution reduces the Bernoulli equation dy/dx+P(x)y=Q(x)yn to a linear equation?

  1. v=yn
  2. v=y1-n
  3. v=ny
  4. v=y/x

Answer

B. v=y1-n

Solution

Divide by yn and let v=y1-n. Then dv/dx=(1-n)y-ndy/dx and the equation becomes dv/dx+(1-n)P,v=(1-n)Q, which is linear in v.

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