CUET · MATHS · PYQ PAPER 2023
Particular solution of the differential equation \(\log \left(\frac{d y}{d x}\right)=x+y\) given that when x = 0 y = 0 is:
- A \(e^x+e^{-y}=2\)
- B \(e^{-x}+e^y=2\)
- C \(e^x+e^y=2\)
- D \(e^{-x}+e^{-y}=2\)
Answer & Solution
Correct Answer
(A) \(e^x+e^{-y}=2\)
Step-by-step Solution
Detailed explanation
\(\frac{dy}{dx} = e^{x+y} = e^x e^y\) \(e^{-y} dy = e^x dx\) \(\int e^{-y} dy = \int e^x dx\) \(-e^{-y} = e^x + C\) Substitute \(x=0, y=0\): \(-e^0 = e^0 + C \Rightarrow -1 = 1 + C \Rightarrow C = -2\) \(-e^{-y} = e^x - 2\) \(e^x + e^{-y} = 2\)
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