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COMEDK2017MathematicsDifferential Equations

The differential equation of y=a e^ b x+c is

Options

  1. Ay₂=y₁+y
  2. By₂²=y y₁
  3. Cy₁²=y y₂
  4. Dy²=y₁ y₂

Correct answer

C. y₁²=y y₂

Step-by-step solution

We have, y=a e^ b x+c ...(i) Differentiating Eq. (i) w.r.t. x , we get y₁=a (e^ b x+c ) b=b (a e^ b x+c )=b y...(ii) Again differentiating Eq. (ii) w.r.t. x , we get y₂=b y₁...(iii) From Eq. (iii) and Eq. (i), we have y y₂=y₁²

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