The differential equation of the family of curves given by $y=a e^{2 x}+b e^{5 x}$ where $a$ and $b$ are parameters is

• A

  $\frac{d^2 y}{d x^2}+7 \frac{d y}{d x}-10 y=0$
• Correct answer
  B

  $\frac{d^2 y}{d x^2}-7 \frac{d y}{d x}+10 y=0$
• C

  $\frac{d^2 y}{d x^2}-7 \frac{d y}{d x}+12 y=0$
• D

  $\frac{d^2 y}{d x^2}-10 \frac{d y}{d x}+7 y=0$

Hence, the correct answer is option: 'B'.