A homogeneous differential equation of the form M(x, y) dx + N(x, y) dy = 0 can be reduced to a differential equation with separated variables by using the substitution?

A homogeneous differential equation of the form M(x, y) dx + N(x, y) dy = 0 can be reduced to a differential equation with separated variables by using the substitution?

Explanation
  • The correct answer is: y = vx, dy = vdx + xdv
  • This substitution is used to solve homogeneous differential equations, as it allows for the separation of variables.
  • By substituting y = vx and dy = vdx + xdv, the original equation can be transformed into a separable equation, which can then be solved by integrating both sides separately.