who to identify that the given differential equation is homogeneous and linear

Question

anonymous · Answer

I think it was homogenous if it didnt have a constant in the equation. And its linear if it doesnt have any of the $y^2, y^3$ etc. or $y'*y$ or $y'^2$. I'm not sure if $x^2$ parts ruins the linearity of the equation.

anonymous · Answer

can you tell me what homogeneous equation actually means

anonymous · Answer

http://en.wikipedia.org/wiki/Homogeneous_differential_equation

mathmate · Answer

Linear: the equation contains only y' or y terms, without y^2, y^4, (y')^2 etc in the equation. Homogeneous 
Examples: $y′+4x^2y=0$ is a homogeneous differential equation. 
$y′+6x^2y=5 $  is inhomogeneous 
For a linear equation, if you have non-zero terms that do not contain y or y', it is not homogeneous.

anonymous · Answer

the second equation in the example you gave is  linear ?

amistre64 · Answer

there are 2 definitions of homogenous

amistre64 · Answer

the usual definition meaning:  this = 0

the other is:  f(x,y) such that T(tx,ty) = t f(x,y)  or some such