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प्रश्न
The differential equation `y ("d"y)/("d"x) + "c"` represents: ______.
विकल्प
Family of hyperbolas
Family of parabolas
Family of ellipses
Family of circles
उत्तर
The differential equation `y ("d"y)/("d"x) + "c"` represents: Family of circles.
Explanation:
Given differential equation is `y ("d"y)/("d"x) + x` = c
⇒ `y ("d"y)/("d"x)` = c – x
⇒ ydy = (c – x)dx
∴ Integrating both sides, we get
`int y "d"y = int ("c" - x) "d"x`
⇒ `y^2/2 = "c"x - x^2/2 + "k"`
⇒ `x^2/2 + y^2/2 - "c"x` = k
⇒ x2 + y2 – 2cx = 2k which is a family of circles.
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