Differential Equations Question 44
Question: Solution of $ ydx-xdy=x^{2}ydx $ is
[MP PET 1999]
Options:
A) $ y{e^{x^{2}}}=cx^{2} $
B) $ y{e^{-x^{2}}}=cx^{2} $
C) $ y^{2}{e^{x^{2}}}=cx^{2} $
D) $ y^{2}{e^{-x^{2}}}=cx^{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
Given equation can be written as $ ( \frac{1-x^{2}}{x} )dx=\frac{dy}{y} $
After integration, we get $ \log x-\frac{x^{2}}{2}=\log y+\log c $
Therefore $ \log x^{2}-\log y^{2}+\log c=x^{2} $
Therefore $ \log \frac{cx^{2}}{y^{2}}=x^{2}$
Therefore $ \frac{cx^{2}}{y^{2}}=e^{x^{2}} $
Therefore $ cx^{2}=y^{2}{e^{x^{2}}} $ .
BETA
