Check documentation for SolveAlways. That might be what you want here. If not, then you are asking for more than you can get (literally), since one equation will not suffice to solve for two unknowns.
SolveAlways
I’ll try that, thank you! What does it do exactly?
Hi Eric,
For situations like this, try Reduce.
Reduce
Reduce[c1*E^x + c2*x*E^x == 0, {c1, c2}] (* (x == 0 && c1 == 0) || (x != 0 && c2 == -(c1/x)) *)
