# Thread: why isn't this problem homogeneous?

1. ## why isn't this problem homogeneous?

ok i have this problem:

dy/dx = (-y+10)/(x+1)

i see that it is separable and exact, but why isn't this problem homogeneous? isn't everything to the power of 1?

in the next problem i have the same issue.

dy/dx = 1/(x(x-y))

i got this problem wrong as well. i was trying to say that it is a homogeneous equation but my book says its a Bernoulli equation? why

2. Originally Posted by slapmaxwell1
isn't everything to the power of 1?
$\displaystyle -y+10=-y^1+10y^0$ .

in the next problem i have the same issue. dy/dx = 1/(x(x-y))
Your equation is equivalent to $\displaystyle x(x-y)dy-dx=0$ , then $\displaystyle x(x-y)$ is homogeneus of degree $\displaystyle 2$ and $\displaystyle -1$ is homogeneous of degree $\displaystyle 0$ so, the equation is not homogeneous.

Fernando Revilla

3. If your differential equation is of the form

$\displaystyle \dfrac{dy}{dx} = F\left(\dfrac{y}{x}\right)$

for some $\displaystyle F$ then it's homogeneous. Neither of the two equations you give can be put in this form.