# why isn't this problem homogeneous?

• Feb 13th 2011, 02:37 PM
slapmaxwell1
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
• Feb 13th 2011, 02:47 PM
FernandoRevilla
Quote:

Originally Posted by slapmaxwell1
isn't everything to the power of 1?

$-y+10=-y^1+10y^0$ .

Quote:

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

Fernando Revilla
• Feb 14th 2011, 05:21 AM
Jester
If your differential equation is of the form

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

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