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CUET · MATHS · PYQ PAPER 2025

The general solution of the differential equation \(\frac{d y}{d x}=x y+x+y+1\) is

  1. A \(\log _e|y|=x+y+C\), where \(C\) is constant of integration
  2. B \(\log _e|y+1|=\frac{1}{2} x^2+x+C\), where \(C\) is constant of integration
  3. C \(\log _e|x+1|=\frac{1}{2} y^2+y+C\), where \(C\) is constant of integration
  4. D \(\log _e|x|=\frac{1}{2} y^2+y+C\), where \(C\) is constant of integration
Verified Solution

Answer & Solution

Correct Answer

(B) \(\log _e|y+1|=\frac{1}{2} x^2+x+C\), where \(C\) is constant of integration

Step-by-step Solution

Detailed explanation

\(\frac{d y}{d x}=x(y+1)+(y+1)\) \(\frac{d y}{d x}=(x+1)(y+1)\) \(\int \frac{d y}{y+1}=\int (x+1) d x\) \(\log _e|y+1|=\frac{1}{2} x^2+x+C\)