AP EAMCET · Maths · Differential Equations
If \(y=y(x)\) is a particular solution of \(\sqrt{1-x^2} \frac{d y}{d x}+\frac{2 x}{\sqrt{1-x^2}}\) \(y=x, y(0)=1\), then \(y\left(\frac{1}{2}\right)=\)
- A \(\frac{\sqrt{3}}{2}\)
- B \(\frac{1}{4}\)
- C \(\frac{1}{2}\)
- D 0
Answer & Solution
Correct Answer
(A) \(\frac{\sqrt{3}}{2}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {} \because \quad \sqrt{1-\mathrm{x}^2} \frac{\mathrm{dy}}{\mathrm{dx}}+\frac{2 \mathrm{x}}{\sqrt{1-\mathrm{x}^2}} \mathrm{y}=\mathrm{x} \\ & \Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}+\frac{2 \mathrm{x}}{1-\mathrm{x}^2}…
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