Hi maths people I have question for test I write next week. There are differential equations and you say what property they have. But my issue is I maybe don't understand all property right.
For order I count maximum number of derivative line. By this I mean for example $y''' + y''$ maximum line is $3$ so this is 3th order.
Linear you check if exponent of $y$ or $y$ with lines is equal to $1$. Example $(y'')^4$ not linear, $y^2$ not linear, but $y+y''$ is linear.
Homogeneous you check if equation is equal with zero and check if function have.. I call it disturbing function. If it have disturbing function you have no homogenetic. I don't can explain good sorry but here is example:
$y'''+2y'' = 0$ this is homo because equal to zero and no disturbing function.
$y'''-6xy' = 2-3e^x$ this is no homo because there is disturbung function $2$
But I have question, what if this is $y'''-6xy' = 3e^x$ (so without $2$) instead? I think is homogeneous because $x$ and $y$ belong to equation so there is no disturbing function. Is this right?
But what is constant coefficient? I think coefficient is the thing factorized by the variables. When it is number, it is constant coefficient. But I don't know.. can you please give example?
Here is summary I make examples (can you say if this is right?):
$y''' +2y'' -5y'+3y+2=0$, 3th order, linear, constant coefficients, no homo
$2xy+x^2y'=0$, 1st order, linear, no constant coefficients because muliply by $x$, homo
Can you please say if all is good? My friend also not sure we learn together and this is only thing we must understanded then ready for test in school! Thank you very much for read all my question!!