  \]

  We arrived at this contradiction because we incorrectly divided both
  sides of the equation by \( a - b \) even though \( a - b = 0 \).
</p>
<h2 id="differential-equation">Differential Equation</h2>
<p>
  We need to be careful about division by zero while solving
  differential equations too.
</p>
<p>
  Consider the differential equation

  \[
    y' = x^2 y^2.
  \]

  Dividing both sides by \( y^2 \), the variables separate and we get

  \[
    y^{-2} y' = x^2.
  \]

  Integrating both sides with 