AP EAMCET · Maths · Differential Equations
The solution of \(\left(x^2+y^2\right) d x=2 x y d y\) is :
- A \(c\left(x^2-y^2\right)=x\)
- B \(c\left(x^2+y^2\right)=x\)
- C \(c\left(x^2-y^2\right)=y\)
- D \(c\left(x^2+y^2\right)=y\)
Answer & Solution
Correct Answer
(A) \(c\left(x^2-y^2\right)=x\)
Step-by-step Solution
Detailed explanation
\(\because \quad \frac{x^2+y^2}{2 x y}=\frac{d y}{d x}\) Put \(y=v x\) and \(\frac{d y}{d x}=v+x \frac{d v}{d x}\) \(\therefore \quad v+x \frac{d v}{d x}=\frac{x^2+v^2 x^2}{2 x^2 v}\) \(\Rightarrow \quad v+x \frac{d v}{d x}=\frac{1+v^2}{2 v}\)…
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