Question

Identify the statement(s) which is/are True.

• A. $f(x,y)=e^{y/x}+\tan \frac{y}{x}$ is homogeneous of degree zero
• B. $x.\ln \frac{y}{x}dx+\frac{y^2}{x}{\sin }^{-1}\frac{y}{x}dy=0$ is homogeneous of degree one
• C. $f(x,y)=x^2+\sin x.\cos y$ is not homogeneous
• D. $(x^2+y^2)dx-({xy}^2-y^3)dy=0$ is a homogeneous differential equation.

Answer 1

Answer: (A), (C)

The correct options are
A $f(x,y)=e^{y/x}+\tan \frac{y}{x}$ is homogeneous of degree zero
C $f(x,y)=x^2+\sin x.\cos y$ is not homogeneous

A. $f\left(x,y\right)=\left(e^{y/x}+\tan \frac{y}{x}\right)$ is homogeneous and degree is zero.

B. Homogeneity cannot be establish

D. Same