Engineering Board Exam Reviewer · Exact Differential Equations · medium

Find the value of k that makes (2xy+ky2),dx+(x2+2xy),dy=0 exact.

1. 1
2. 2
3. 0
4. -1

Answer

A. 1

Solution

With M=2xy+ky2 and N=x2+2xy: M/ y=2x+2ky and N/ x=2x+2y. Setting these equal gives k=1.

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