Show substitution leads to a separable differential equation.

Consider the differential equation...

${y}^{\prime}=f(\frac{y}{t})$

Show that the substitution $v=\frac{v}{t}$ leads to a separable differential equation in v

Here's what I did.

$v=\frac{y}{t}$

$\frac{dv}{dt}=\frac{dy}{dt}-\frac{1}{{t}^{2}}$

Sub into the orignal.

$\frac{dv}{dt}=f(v)-\frac{1}{{t}^{2}}$

$\frac{dv}{f(v)}=\frac{1}{{t}^{2}}dt$

This is where I get stuck. Is this the what the question is asking for, or am I forgetting to do something?

Consider the differential equation...

${y}^{\prime}=f(\frac{y}{t})$

Show that the substitution $v=\frac{v}{t}$ leads to a separable differential equation in v

Here's what I did.

$v=\frac{y}{t}$

$\frac{dv}{dt}=\frac{dy}{dt}-\frac{1}{{t}^{2}}$

Sub into the orignal.

$\frac{dv}{dt}=f(v)-\frac{1}{{t}^{2}}$

$\frac{dv}{f(v)}=\frac{1}{{t}^{2}}dt$

This is where I get stuck. Is this the what the question is asking for, or am I forgetting to do something?