Question

Which substitutions are chosen for a homogeneous differential equation?

Options

• \[y=\frac{v}{x}\] or \[x=\frac{v}{y}\]

• \[y=vx^{2}\] or \[x=vy^{2}\]

• \[y=vx\] or \[x=vy\]

• \[y=v+x\] or \[x=v+y\]

Answer 1

The substitutions used are \[y=vx\] and \[x=vy\]. They replace a dependence on \[\frac{y}{x}\] or \[\frac{x}{y}\] by a dependence on \[v\].