Differential Equations Question 108
Question: The differential equation corresponding to primitive $ y=e^{cx} $ is or The elimination of the arbitrary constant m from the equation $ y=e^{mx} $ gives the differential equation
[MP PET 1995, 2000; Pb. CET 2000]
Options:
A) $ \frac{dy}{dx}=( \frac{y}{x} )\log x $
B) $ \frac{dy}{dx}=( \frac{x}{y} )\log y $
C) $ \frac{dy}{dx}=( \frac{y}{x} )\log y $
D) $ \frac{dy}{dx}=( \frac{x}{y} )\log x $
Show Answer
Answer:
Correct Answer: C
Solution:
$ y=e^{mx} $
Therefore $ \log y=mx\Rightarrow m=\frac{\log y}{x} $
Now $ y=e^{mx} $
Therefore $ \frac{dy}{dx}=me^{mx}=\frac{\log y}{x}.y=( \frac{y}{x} )\log y $ .
BETA
