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NTA Abhyas JEE Main2020MathematicsDifferential EquationsPractice

A curve is such that the slope of the tangent to it at any point P is the product of ordinate of P and abscissa increased by 2. If it passes through - 4 , e , then its equation is

Options

  1. Ay = x 2 - 16 + e
  2. Bx y + 4 e = 0
  3. Cy = e x 2 2 + 2 x + 1
  4. Dy = e x + 5

Correct answer

C. y = e x 2 2 + 2 x + 1

Step-by-step solution

d y d x = y x + 2 ⇒ ∫ d y y = ∫ x + 2 d x ⇒ ln ⁡ y = x 2 2 + 2 x + c ⇒ y = e x 2 2 + 2 x + c As it passes through - 4 , e ⇒ c = 1 ∴ Equation of the curve is y = e x 2 2 + 2 x + 1

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