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

False

Definition :- If $f(tx,ty)=t^nf(x,y)$ then $f(x,y)$ is called homogeneous function of degree $n$ $f(x,y)=\Large\frac{y^2+x}{x^2+2y^2}$ $f(tx,ty)=\Large\frac{t^2y^2+tx}{t^2(x^2+2y^2)}$ $f(tx,ty)\neq t^nf(x,y)$ for any $n$ Therefore $f(x,y)$ is not homogeneous function.