Engineering Board Exam Reviewer · Homogeneous First-Order Equations · easy

Find the general solution of dy/dx=x+y/x for x>0.

1. y = C + x x
2. y = C x x
3. y = C x + x x
4. y = C x + x

Answer

C. y = C x + x x

Solution

Let y=vx: v+xdv/dx=1+v /dx= 1x v= x+C, so y=x x+Cx.

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