Question

Which values of k and t can make y'=a*(x^k)+b*(y^t) a homogeneous equation with the help of y=z^m

Answer 1

If $y=x^m$ , then:

$mx^{m-1}=ax^k+bx^{mt}$

Condition for a homogeneous equation:

$m-1=k=mt$

So:

$k=m-1, t=\frac{m-1}{m}$