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Question

The differential equation formed by eliminating arbitrary constants from y = Ae^x + Be^(-x) is

RankGuru · Accepted Answer

1. **Identify Number of Constants**: There are 2 constants ($A, B$), so we need two differentiations.
2. **First Derivative**:
   - $y' = A e^x - B e^{-x}$
3. **Second Derivative**:
   - $y'' = A e^x + B e^{-x}$
4. **Eliminate Constants**: Notice that the right-hand side of $y''$ is identical to the original function $y$.
   - $y'' = y \implies y'' - y = 0$.
5. **Standard Notation**: $\frac{d^2y}{dx^2} - y = 0$.

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