Engineering Board Exam Reviewer · Exact Differential Equations · hard
Solve (2x+y),dx+(x-2y),dy=0 with y(1)=2 and find y(2).
- 3.45
- -1.45
- 3
- 4
Answer
A. 3.45
Solution
My=1=Nx, so the equation is exact with F=x2+xy-y2=C. With y(1)=2: C=1+2-4=-1. At x=2: 4+2y-y2=-1 y2-2y-5=0 y=1 6. The branch through (1,2) is y=1+ 6 3.45.
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