Question

If y = 500 e^7x + 600 e^−7x, show that $\frac{d^{2}y}{d{x}^2}=49y$.

Answer 1

Here,

$$\begin{gathered} y=500e^{7x}+600e^{-7x} \\ \mathrm{Differentiating}\mathrm{w}.\mathrm{r}.\mathrm{t}.x\mathit{,}\mathit{}\mathrm{we}\mathrm{get} \\ \frac{\mathit{d}\mathit{y}}{\mathit{d}\mathit{x}}=3500e^{7x}-4200e^{-7x} \\ \mathrm{Differentiating}\mathrm{again}\mathrm{w}.\mathrm{r}.\mathrm{t}.x\mathit{,}\mathit{}\mathrm{we}\mathrm{get} \\ \frac{{\mathit{d}}^{\mathit{2}}\mathit{y}}{\mathit{d}{\mathit{x}}^{\mathit{2}}}=24500e^{7x}+29400e^{-7x} \\ =49\left(500e^{7x}+600e^{-7x}\right)=49y \end{gathered}$$