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COMEDK2024MathematicsDifferential Equations

The general solution of d y d x =1+x+y+x y , y=

Options

  1. Ak e^ x+ x^2 2 -1
  2. Bk e^ x- x^2 2 +1
  3. Ck e^ 1+ x^2 2 -1
  4. Dk e^ 1- x^2 2 +1

Correct answer

A. k e^ x+ x^2 2 -1

Step-by-step solution

We have, aligned & d y d x =1+x+y(1+x) & d y d x =(1+x)(1+y) & d y 1+y =(1+x) d x aligned Integrate both sides, aligned d y 1+y & = (1+x) d x (1+y) & =x+ x^2 2 +C [ 1 t d t= t+C ] 1+y & =e^ x+ x^2 2 e^C y & =k e^ x+ x^2 2 -1 [ e^c=k (Constant) ] aligned

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