Chapter 1 - First-Order Differential Equations - 1.8 Change of Variables - True-False Review - Page 78: a

True

Definition :- If $f(tx,ty)=t^nf(x,y)$ then $f(x,y)$ is called homogeneous function of degree $n$ $f(x,y)=\Large\frac{3y^2-5xy}{2xy+y^2}$ $f(tx,ty)=\Large\frac{t^2(3y^2-5xy)}{t^2(2xy+y^2)}$ $f(tx,ty)=t^0f(x,y)$ $\Rightarrow f(x,y)$ is homogeneous function of degree 0.