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NTA Abhyas JEE Main2020MathematicsDifferential EquationsPractice

The slope of the tangent at any arbitrary point of a curve is twice the product of the abscissa and square of the ordinate of the point. Then, the equation of the curve is (where c is an arbitrary constant)

Options

  1. Ax 2 y + y + c = 0
  2. Bx 2 y + c y + 1 = 0
  3. Cx y + y + c = 0
  4. Dx y 2 + c y + y = 0

Correct answer

B. x 2 y + c y + 1 = 0

Step-by-step solution

Given, d y d x = 2 y 2 x ⇒ ∫ d y y 2 = ∫ 2 x     d x or - 1 y = x 2 + c or x 2 y + c y + 1 = 0

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