Question

Which dependence is checked on the right-hand side of a homogeneous differential equation?

Options

• Only on \[\frac{dy}{dx}\] or \[\frac{dx}{dy}\]

• Only on \[x+y\] or \[x-y\]

• Only on \[\frac{y}{x}\] or \[\frac{x}{y}\]

• Only on \[xy\] or \[\frac{1}{xy}\]

Answer 1

The right-hand side is checked to see whether it depends only on \[\frac{y}{x}\] or \[\frac{x}{y}\]. This determines whether \[y=vx\] or \[x=vy\] is the suitable substitution.