Differential Equations Question 240
Question: The solution of the equation $ \frac{dy}{dx}=\sqrt{\frac{1-y^{2}}{1-x^{2}}} $ is
Options:
A) $ {{\sin }^{-1}}y-{{\sin }^{-1}}x=c $
B) $ {{\sin }^{-1}}y{{\sin }^{-1}}x=c $
C) $ {{\sin }^{-1}}(xy)=2 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ \frac{dy}{dx}=\sqrt{\frac{1-y^{2}}{1-x^{2}}}\therefore \frac{dy}{\sqrt{1-y^{2}}}=\frac{dx}{\sqrt{1-x^{2}}} $
$ \Rightarrow \int{\frac{dy}{\sqrt{1-y^{2}}}=\int{\frac{dx}{\sqrt{1-x^{2}}}}\Rightarrow {{\sin }^{-1}}y={{\sin }^{-1}}x+c} $
$ \therefore {{\sin }^{-1}}y-{{\sin }^{-1}}x=c $
BETA
