For each of the following equations, state the order and whether it is linear inhomogeneous, linear homogeneous or nonlinear.
$a) u_t - u_{xx} +1 =0$
$b) u_t - u_{xx} + xu =0$
$c) u_t - u_{xxt}+uu_x =0$
$d) u_{tt} - u_{xx} +x^2 = 0$
$e) (cosx)u_x + u_y = u^2$
$f) u_x - e^xu_y = cosx$
$g) u_{tt} - u_{xx} +e^uu_x =0$
My attempts, in the above order are, a) 2nd order linear homogeneous (a bit skeptical and think this might be nonlinear because of the 1), b) 2nd order linear homogeneous, c) 3rd order nonlinear, d) 2nd order nonlinear, e) 1st order nonlinear(perhaps linear in-homogeneous) f) 1st order linear in-homogeneous, g) 2nd order linear homogeneous. Can someone please help me verify these answers. How would one identify if the equation is nonlinear or linear as that would throw me off a bit when trying to finish this problem. Any help would be greatly appreciated.