CUET · MATHS · PYQ PAPER 2025
The general solution of the differential equation \(\frac{d y}{d x}=e^{x-y}+x^2 e^{-y}\) is equal to:
- A \(e^y=e^x+\frac{x^3}{3}+c\), where \(c\) is an arbitrary constant.
- B \(e^y=x e^x+\frac{x^2}{3}+c\), where \(c\) is an arbitrary constant.
- C \(e^y=2 e^x+\frac{x^2}{4}+c\), where \(c\) is an arbitrary constant.
- D \(y=e^x+\frac{x^3}{3}+c\), where \(c\) is an arbitrary constant.
Answer & Solution
Correct Answer
(A) \(e^y=e^x+\frac{x^3}{3}+c\), where \(c\) is an arbitrary constant.
Step-by-step Solution
Detailed explanation
\(e^y dy=(e^x+x^2) dx\) \(\int e^y dy = \int (e^x+x^2) dx\) \(e^y = e^x + \frac{x^3}{3} + c\)
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