AP EAMCET · Maths · Differential Equations
Solve the differential equation given below
\[
\frac{x d y}{d x}=y+\sqrt{x^2+y^2}
\]
- A \(x^2=c\left[y+\sqrt{y^2+x^2}\right]\)
- B \(y^2=c\left[x+\sqrt{y^2-x^2}\right]\)
- C \(y^2=c\left[x+\tan ^{-1}\left(\sqrt{1+y^2}\right)\right]\)
- D \(y^2=c\left[x-\sqrt{y^2+x^2}\right]\)
Answer & Solution
Correct Answer
(A) \(x^2=c\left[y+\sqrt{y^2+x^2}\right]\)
Step-by-step Solution
Detailed explanation
Given differential equation \[ \begin{aligned} \quad x \frac{d y}{d x} & =y+\sqrt{x^2+y^2} \\ \Rightarrow \quad \frac{d y}{d x} & =\frac{y+\sqrt{x^2+y^2}}{x} \end{aligned} \] Now, put \(y=v \cdot x\) \[ \therefore \quad \frac{d y}{d x}=v+x \frac{d v}{d x} \] On doing…
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