Question:
Show that the differential equation ydy/dx x = C represents family of circles.
Answer:
Given, y(dy/dx) + x = C
=> y(dy/dx) = C - x
=> y*dy = (C - x)dx
Now, integrate on both side, we get
∫y*dy = ∫(C - x)dx
=> y2 /2 = Cx - x2 /2
=> y2 /2 + x2 /2 = Cx
=> (y2 + x2 )/2 = Cx
=> x2 + y2 = 2Cx
=> x2 + 2Cx + y2 = 0
So, it represents an equation of family of circles.
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