Differential Equations Question 85
Question: The solution of $ (x-y^{3})dx+3xy^{2}dy=0 $ is
Options:
A) $ \log x+\frac{x}{y} $
B) $ \log x+\frac{y^{3}}{x}=k $
C) $ \log x-\frac{x}{y^{3}}=k $
D) $ \log xy-y^{3}=k $
Show Answer
Answer:
Correct Answer: B
Solution:
$ xdx-y^{3}dx+3xy^{2}dy=0 $
Put $ y^{3}=t $
$ \Rightarrow $ $ dt=3y^{2}dy $
$ xdx-tdx+xdt=0 $
Therefore $ xdx+xdt-tdx=0 $
Therefore $ \frac{dx}{x}+d( \frac{t}{x} )=0 $
On integration, we get $ \log x+\frac{t}{x}=k $
Therefore $ \log x+\frac{y^{3}}{x}=k $ .
BETA
