हिंदी

The differential equation ddcydydx+c represents: ______. - Mathematics

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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

MCQ
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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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अध्याय 9: Differential Equations - Exercise [पृष्ठ १९७]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
अध्याय 9 Differential Equations
Exercise | Q 49 | पृष्ठ १९७

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