Engineering Board Exam Reviewer · Exact Differential Equations · easy

Solve (3x2y+2),dx+(x3+4y),dy=0.

  1. x3 y + 2 x + 4 y2 = C
  2. x3 y + 2 x + y2 = C
  3. x3 y + 2 x + 2 y2 = C
  4. 3 x2 y + 2 x + 2 y2 = C

Answer

C. x3 y + 2 x + 2 y2 = C

Solution

My=3x2=Nx, so the equation is exact. F= (3x2y+2),dx=x3y+2x+g(y) and Fy=x3+g'(y)=x3+4y g=2y2. Solution: x3y+2x+2y2=C.

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