Engineering Board Exam Reviewer · Exact Differential Equations · medium

Solve the exact differential equation (3x2+2y),dx+(2x+3y2),dy=0.

  1. x3+2xy+y3=C
  2. x3+xy+y3=C
  3. x2+2xy+y2=C
  4. x3-2xy+y3=C

Answer

A. x3+2xy+y3=C

Solution

Seeking F(x,y) with Fx=3x2+2y and Fy=2x+3y2 gives F=x3+2xy+y3+C1, so the solution is x3+2xy+y3=C.

More Exact Differential Equations questions

  1. Determine whether (y x+2xey),dx+( x+x2ey),dy=0 is exact.
  2. Find the value of k that makes (2xy+ky2),dx+(x2+2xy),dy=0 exact.
  3. Determine whether (2xy),dx+(x2+1),dy=0 is an exact differential equation.
  4. Solve the exact differential equation (2xy),dx+(x2+1),dy=0.
  5. Determine whether (3x2+2y),dx+(2x+3y2),dy=0 is exact.

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