WBJEE · Maths · Differential Equations
The general solution of the differential equation \(\log _{\mathrm{e}}\left(\frac{d y}{d x}\right)=x+y\) is
- A \(e^x+e^{-y}=C\)
- B \(e^x+e^y=C\)
- C \(e^y+e^{-x}=C\)
- D \(e^{-x}+e^{-y}=C\)
Answer & Solution
Correct Answer
(A) \(e^x+e^{-y}=C\)
Step-by-step Solution
Detailed explanation
Hints: \(\frac{d y}{d x}=e^x \cdot e^y \Rightarrow \int e^{-y} d y .=\int e^x d x \Rightarrow e^x+e^{-y}=c\)
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