COMEDK · Maths · 32. Differential Equations
The solution of the differential equation \(\dfrac{d y}{d x}+\sqrt{\dfrac{1-y^2}{1-x^2}}=0\) is
- A \(\cos ^{-1} x+\cos ^{-1} y=c \quad\)
- B \(\sin ^{-1} x+\sin ^{-1} y=c\)
- C \(\cosh ^{-1} x+\cosh ^{-1} y=c\)
- D \(\sinh ^{-1} x+\sinh ^{-1} y=c\)
Answer & Solution
Correct Answer
(B) \(\sin ^{-1} x+\sin ^{-1} y=c\)
Step-by-step Solution
Detailed explanation
The given differential equation is \(\dfrac{dy}{dx} + \sqrt{\dfrac{1-y^2}{1-x^2}} = 0\). Separating the variables, we get \(\dfrac{dy}{\sqrt{1-y^2}} = -\dfrac{dx}{\sqrt{1-x^2}}\). Integrating both sides, we have \(\int \dfrac{dy}{\sqrt{1-y^2}} = -\int \dfrac{dx}{\sqrt{1-x^2}}\).…
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