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

False

Definition:- Differential equation $\Large\frac{dy}{dx}$=$f(x,y)$ is called homogeneous differential equation if $f(x,y)$ is homogeneous function. Here $\;\;f(x,y)=\Large\frac{x^3+xy^2}{y^3+1}$ $f(tx,ty)=\Large\frac{t^3(x^3+xy^2)}{t^3y^3+1}$ $f(tx,ty)\neq t^nf(x,y)\;\;$ for any $n$ $\Rightarrow f(x,y)$ is not homogeneous function That's why given differential equation is not homogeneous.