Differential-Equations Question 367
Question: Solution of differential equation $ \frac{dy}{dx}=2xy $ is
[MP PET 1997]
Options:
A) $ y=c{e^{x^{2}}} $
B) $ y^{2}=2x^{2}+c $
C) $ y={e^{-x^{2}}}+c $
D) $ y=x^{2}+c $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \int_{{}}^{{}}{\frac{dy}{y}=\int_{{}}^{{}}{2xdx}} $
Þ $ {\log_{e}}y=x^{2}+c $
Þ $ y={e^{x^{2}+c}}=e^{c}{e^{x^{2}}} $
Þ $ y=c{e^{x^{2}}} $ .
BETA
