AP EAMCET · Maths · Differential Equations
The general solution of the differential equation \((x+y) y d x+(y-x) x d y=0\) is
- A \(x+y \log (c y)=0\)
- B \(\frac{y}{x}=\log (x y)+c\)
- C \(x+y \log (c x y)=0\)
- D \(\frac{y}{x}=\log (c x y)\)
Answer & Solution
Correct Answer
(C) \(x+y \log (c x y)=0\)
Step-by-step Solution
Detailed explanation
\(y=v x\) \(\frac{d y}{d x}=v+x \frac{d v}{d x} \Rightarrow(x+y) y d x=(x-y) x d y\) \(\frac{d y}{d x}=\frac{(x+y) y}{(x-y) x} \Rightarrow v+x \frac{d v}{d x}=\frac{(x+v x) v x}{(x-v x) x}=\frac{v^2+v}{1-v}\) \(x \frac{d v}{d x}=\frac{v^2+v}{1-v}-v=\frac{2 v^2}{1-v}\)…
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