Differential Equations Question 14
Question: The solution of the differential equation $ (x-y^{2}x)dx=(y-x^{2}y)dy $ is
[DSSE 1984]
Options:
A) $ (1-y^{2})=c^{2}(1-x^{2}) $
B) $ (1+y^{2})=c^{2}(1-x^{2}) $
C) $ (1+y^{2})=c^{2}(1+x^{2}) $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Given equation can be written as $ \frac{x}{1-x^{2}}dx=\frac{y}{1-y^{2}}dy $
On integrating we get $ -\frac{1}{2}\log (1-x^{2})=-\frac{1}{2}\log (1-y^{2})+\log c $
Therefore $ \log (1-x^{2})-\log (1-y^{2})=-2\log c $
Therefore $ \frac{1-x^{2}}{1-y^{2}}={c^{-2}} $
Hence $ (1-y^{2})=c^{2}(1-x^{2}) $ .
BETA
