Engineering Board Exam Reviewer · Linear First-Order Differential Equations · hard

Find the general solution of dy/dx=1/x+y.

1. x = C ey + y + 1
2. x = C e- y - y - 1
3. y = C ex - x - 1
4. x = C ey - y - 1

Answer

D. x = C ey - y - 1

Solution

This is not linear in y, but it is linear in x: dx/dy=x+y /dy-x=y. The integrating factor is e-y: d/dy≤ft(xe-y )=ye-y xe-y=-ye-y-e-y+C. So x=Cey-y-1.

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