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CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsCONTINUITY AND DIFFERENTIABILITY2 Marks
Question
$\text{If y}=500\text{e}^{7\text{x}}+600\text{e}^{-7\text{x}},\text{ show that }\frac{\text{d}^2\text{y}}{\text{dx}^2}=49\text{y}$
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Answer

 $\text{y}=500\text{e}^{7\text{x}}+600\text{e}^{-7\text{x}}\dots(1)$
$\frac{\text{dy}}{\text{dx}}=3500\text{e}^{7\text{x}}-4200\text{e}^{-7\text{x}}$
 $\frac{\text{d}^2\text{y}}{\text{dx}^2}=24500\text{e}^{7\text{x}}+29400\text{e}^{-7\text{x}}$
$\Rightarrow\ \frac{\text{d}^2\text{y}}{\text{dx}^2}=49(500\text{e}^{7\text{x}}+600\text{e}^{-7\text{x}})$
$\Rightarrow\ \frac{\text{d}^2\text{y}}{\text{dx}^2}=49\text{y}\ \ [\because\text{of }1]$

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