COMEDK · Maths · 32. Differential Equations
The solution of the differential equation: \(x \cos y d y=\left(x e^x \log x+e^x\right) d x\) is
- A \(\sin y=\dfrac{e^x}{x}+c\)
- B \(\sin y=e^x+\log x+c\)
- C \(\sin y=e^x \log x+c\)
- D \(\sin y-e^x \log x=c\)
Answer & Solution
Correct Answer
(C) \(\sin y=e^x \log x+c\)
Step-by-step Solution
Detailed explanation
The given differential equation is \(x \cos y \, dy = (x e^x \log x + e^x) \, dx\). Rearranging the terms to separate the variables, we have \(\cos y \, dy = \dfrac{x e^x \log x + e^x}{x} \, dx\). Simplifying the right side, we get…
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