CUET · MATHS · PYQ PAPER 2025
The general solution of the differential equation \(e^x d y+\left(y e^x+2 x\right) d x=0\) is
- A \(x e^y+x^2=C\), where C is constant of integration
- B \(x e^y+y^2=C\), where \(C\) is constant of integration
- C \(y e^x+x^2=C\), where C is constant of integration
- D \(y e^y+x^2=C\), where \(C\) is constant of integration
Answer & Solution
Correct Answer
(C) \(y e^x+x^2=C\), where C is constant of integration
Step-by-step Solution
Detailed explanation
\(e^x d y+\left(y e^x+2 x\right) d x=0\) \(e^x d y+y e^x d x = -2 x d x\) \(d(y e^x) = -2x d x\) \(\int d(y e^x) = \int -2x d x\) \(y e^x = -x^2 + C\) \(y e^x + x^2 = C\)
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