AP EAMCET · Maths · Differential Equations
The solution of \(x d y-y d x=\sqrt{x^2+y^2} d x\) when \(y(\sqrt{3})\) \(=1\) is
- A \(y^2+\sqrt{x^2+y^2}=x^2\)
- B \(5 y-\sqrt{x^2+y^2}=x^2\)
- C \(y+\sqrt{x^2+y^2}=x\)
- D \(5 y^2-\sqrt{x^2+y^2}=x\)
Answer & Solution
Correct Answer
(C) \(y+\sqrt{x^2+y^2}=x\)
Step-by-step Solution
Detailed explanation
Since, \(x d y-y d x=\sqrt{x^2+y^2} d x\) \(\begin{aligned} & \Rightarrow x d y=\left(y+\sqrt{x^2+y^2}\right) d x \\ & \Rightarrow \frac{d y}{d x}=\frac{y+\sqrt{x^2+y^2}}{x} \end{aligned}\) Let \(y=v x \Rightarrow \frac{d y}{d x}=v+x \frac{d v}{d x}\) So,…
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