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प्रश्न
If y = 500 e7x + 600 e−7x, show that \[\frac{d^2 y}{d x^2} = 49y\] ?
उत्तर
Here,
\[y = 500 e^{7x} + 600 e^{- 7x} \]
\[\text { Differentiating w . r . t . x, we get }\]
\[\frac{d y}{d x} = 3500 e^{7x} - 4200 e^{- 7x} \]
\[ \text { Differentiating again w . r . t . x, we get}\]
\[\frac{d^2 y}{d x^2} = 24500 e^{7x} + 29400 e^{- 7x} \]
\[ = 49\left( 500 e^{7x} + 600 e^{- 7x} \right) = 49y\]
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