Question

$(1+e^{\frac{x}{y}})dx+e^{\frac{x}{y}}(1-\frac{x}{y})dy=0$ is homogeneous equation

• A. True
• B. False

Answer 1

The correct option is A True

A differential equation of the form $\frac{dy}{dx}=f(x,y)$ if

$f(tx,ty)=t^{0}f(x,y)=f(x,y)$

Here,

$\frac{dy}{dx}=\frac{-1-e^{\frac{x}{y}}}{e^{\frac{x}{y}}(1-\frac{x}{y})}$

So,

$f(x,y)=\frac{-1-e^{\frac{x}{y}}}{e^{\frac{x}{y}}(1-\frac{x}{y})}$

which satisfies

$f(tx,ty)=f(x,y)$

So, the given equation is homogeneous.