y = e^ cx નું વિકલ સમીકરણ મેળવો. - Vidyadip

MCQ

$y = {e^{cx}}$ નું વિકલ સમીકરણ મેળવો.

A
$\frac{{dy}}{{dx}} = \left( {\frac{y}{x}} \right)\log x$
B
$\frac{{dy}}{{dx}} = \left( {\frac{x}{y}} \right)\log y$
✓
$\frac{{dy}}{{dx}} = \left( {\frac{y}{x}} \right)\log y$
D
$\frac{{dy}}{{dx}} = \left( {\frac{x}{y}} \right)\log x$

✓

Answer

Correct option: C.

$\frac{{dy}}{{dx}} = \left( {\frac{y}{x}} \right)\log y$

(c) $y = {e^{mx}}$ ==> $\log y = mx \Rightarrow m = \frac{{\log y}}{x}$

Now $y = {e^{mx}}$ ==> $\frac{{dy}}{{dx}} = m{e^{mx}} = \frac{{\log y}}{x}.y = \left( {\frac{y}{x}} \right)\log y$.

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