Question
यदि $y = a{e^{mx}} + b{e^{ - mx}}$, तो $\frac{{{d^2}y}}{{d{x^2}}} - {m^2}y = $
$\therefore \frac{{dy}}{{dx}} = am{e^{mx}} - mb{e^{ - mx}}$
पुन: अवकलन करने पर, $\frac{{{d^2}y}}{{d{x^2}}} = a{m^2}{e^{mx}} + {m^2}b{e^{ - mx}}$
==> $\frac{{{d^2}y}}{{d{x^2}}} = {m^2}(a{e^{mx}} + b{e^{ - mx}}) \Rightarrow \frac{{{d^2}y}}{{d{x^2}}} = {m^2}y$
या $\frac{{{d^2}y}}{{d{x^2}}} - {m^2}y = 0$.
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$\left[\frac{2^{2020}+1}{2^{2018}+1}\right]+\left[\frac{3^{2020}+1}{3^{2018}+1}\right]+\left[\frac{4^{2020}+1}{4^{2018}+1}\right] +\left[\frac{5^{2020}+1}{5^{2018}+1}\right] + \left[\frac{6^{2020}+1}{6^{2018}+1}\right]$