Differential-Equations Question 368
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 $
Þ $ \log x^{2}-\log y^{2}+\log c=x^{2} $
Þ $ \log \frac{cx^{2}}{y^{2}}=x^{2} $
Þ $ \frac{cx^{2}}{y^{2}}=e^x^{2} $
Þ $ cx^{2}=y^{2}{e^{x^{2}}} $ .
BETA
