Question

ODE: y'=x+y

any solutions?

Answer 1

y=-x-1 is a solution

Answer 2

good, but a more general solution would be with the constant attached right

Answer 3

but i spose i said "any" ;)

Answer 4

y'-y=x /*e^-x
(ye^-x)'=xe^-x
iintegral xe^-x=-e^-x(x+1)+C
so
y=-x-1+C/e^-x