\begin{frame}
  \frametitle{2nd Midterm Exam - Review}

  \begin{exampleblock}{}
    Find constants $A,B,C$ such that $y = Ax^2 + Bx + C$ satisfies
    \begin{align*}
      y'' + y' - 2y = x^2
    \end{align*}
    \pause    
    We have
    \begin{align*}
      y &= Ax^2 + Bx + C & 
      y' &= \mpause[1]{2Ax + B}
      &
      \mpause[2]{y''} &\mpause[2]{=} \mpause[3]{2A}
    \end{align*}
    \pause\pause\pause\pause
    Thus
    \begin{align*}
      x^2 &= y'' + y' - 2y = \mpause[1]{(2Ax + B) + (2A) - 2(Ax^2 + Bx + C)} \\
      &\mpause[2]{= (-2A)x^2 + (2A - 2B)x + (2A + B - 2C)}
    \end{align*}
    \pause\pause\pause
    Hence\vspace{-2ex}
    \begin{align*}
      &-2A = \mpause[1]{1} \mpause[2]{\;\implies\; A = -1/2} \\
      &\mpause[3]{2A - 2B = 0} \mpause[4]{\;\implies\; B = A = -1/2} \\
      &\mpause[5]{2A + B - 2C = 0} \mpause[6]{\;\implies\; C = -3/4} 
    \end{align*}
  \end{exampleblock}
\end{frame}