Differential Equations Question 234
Question: The solution of the differential equation $ y-x\frac{dy}{dx}=a( y^{2}+\frac{dy}{dx} ) $ is
[AISSE 1989, 90]
Options:
A) $ y=c(x+a)(1+ay) $
B) $ y=c(x+a)(1-ay) $
C) $ y=c(x-a)(1+ay) $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ y-x\frac{dy}{dx}=a( y^{2}+\frac{dy}{dx} ) $
Therefore $ y-ay^{2}=(x+a)\frac{dy}{dx} $
Therefore $ \frac{dy}{y(1-ay)}=\frac{dx}{x+a} $
On integrating both sides, we get
Therefore $ \log y-\log (1-ay)=\log (x+a)+\log c $
Therefore $ \frac{y}{(1-ay)}=c(x+a) $ or $ c(x+a)(1-ay)=y $ .
BETA
