CUET · MATHS · PYQ PAPER 2023
The general solution of the differential equation \(\frac{d y}{d x}=\sin ^{-1} x\) is :
- A \(y=x \sin ^{-1} x-\sqrt{1-x^2}+C\), where C is a constant
- B \(y=x \sin ^{-1} x+\sqrt{1}+x^2+C\), where \(C\) is a constant
- C \(y=x \sin ^{-1} x+\sqrt{1-x^2}+C\), where \(C\) is a constant
- D \(y=-x \sin ^{-1} x+\sqrt{1-x^2}+C\), where \(C\) is a constant
Answer & Solution
Correct Answer
(C) \(y=x \sin ^{-1} x+\sqrt{1-x^2}+C\), where \(C\) is a constant
Step-by-step Solution
Detailed explanation
\(y=\int \sin ^{-1} x \, d x\) \(y=x \sin ^{-1} x-\int x \frac{1}{\sqrt{1-x^2}} \, d x\) \(y=x \sin ^{-1} x+\sqrt{1-x^2}+C\)
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