Engineering Board Exam Reviewer · Exact Differential Equations · medium

Solve the exact differential equation (2xy),dx+(x2+1),dy=0.

1. y(x2+1)=C
2. x2y=C
3. xy2=C
4. y(x2-1)=C

Answer

A. y(x2+1)=C

Solution

Seeking F(x,y) with Fx=2xy and Fy=x2+1 gives F=x2y+y+C1, so the solution is y(x2+1)=C.

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