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JEE Main2009MathematicsDifferential EquationsActual

The differential equation which represents the family of curves y=c₁ e^ c₂ x , where c₁ and c₂ are arbitrary constants is

Options

  1. Ay^ =y^2
  2. By^ =y^ y
  3. Cy y^ =y^
  4. Dy y^ = (y^ )^2

Correct answer

D. y y^ = (y^ )^2

Step-by-step solution

aligned & y=c₁ e^ c₂ x & y^ =c₂ c₁ e^ c₂ x & y^ =c₂ y & y^ =c₂ y^ aligned From (2) c₂= y^ y So, y^ = (y^ )^2 y y y^ = (y^ )^2

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