The solution of the differential equation x d x+y d y x d y-y d x = 1- (x^ 2 +y^ 2 ) x^ 2…
Mathematics · JEE Main · NTA Exams — Differential Equations
The solution of the differential equation \(\frac{x d x+y d y}{x d y-y d x}=\frac{\sqrt{1-\left(x^{2}+y^{2}\right)}}{\sqrt{x^{2}+y^{2}}}\) is,
- \(\tan ^{-1} \frac{y}{x}+C=\sin ^{-1} \sqrt{x^{2}+y^{2}}\)
- \(x+\tan ^{-1} \frac{y}{x}+c=\cos ^{-1} x^{2}\)
- \(x+\cot ^{-1}\left(\frac{x}{y}\right)+c=\tan ^{-1} x^{2}\)
- None of these
Answer
(A) ^ -1 y x +C= ^ -1 x^ 2 +y^ 2
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