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