Mathematics · JEE | DIFFERENTIAL EQUATIONS

Consider the following statements regarding differential equations: (A) A homogeneous differential equation of degree zero can always be solved by substituting \( y = vx \). (B) The integrating factor (I.F.) for the linear differential equation \( \frac{dy}{dx} + Py = Q \) is given by \( e^{\int P \, dx} \). (C) The general solution of \( \frac{dy}{dx} + y \cot x = 2x + x^2 \cot x \) contains a logarithmic term. (D) If \( M \, dx + N \, dy = 0 \) is homogeneous, the substitution \( x = vy \) is also valid. Which of the above statements are correct?

1. A
   (A), (B) and (D) only
2. B
   and (C) only
3. C
   (B), (C) and (D) only
4. D
   (A), (B), (C) and (D)