Differential Equations Question 12
Question: The solution of the differential equation $ (1-x^{2})(1-y)dx=xy(1+y)dy $ is
Options:
A) $ \log [x{{(1-y)}^{2}}]=\frac{x^{2}}{2}+\frac{y^{2}}{2}-2y+c $
B) $ \log [x{{(1-y)}^{2}}]=\frac{x^{2}}{2}-\frac{y^{2}}{2}+2y+c $
C) $ \log [x{{(1+y)}^{2}}]=\frac{x^{2}}{2}+\frac{y^{2}}{2}+2y+c $
D) $ \log [x{{(1-y)}^{2}}]=\frac{x^{2}}{2}-\frac{y^{2}}{2}-2y+c $
Show Answer
Answer:
Correct Answer: D
Solution:
$ (1-x^{2})(1-y)dx=xy(1+y)dy $
Therefore $ \int _{{}}^{{}}{\frac{y(1+y)}{(1-y)}dy}=\int _{{}}^{{}}{\frac{(1-x^{2})}{x}dx} $ ; Now integrate it.
BETA
