Question

Algebra legality question.

I've been working on a differential equation and have gotten the general solution: \[y=c_1e ^{t(3+2\sqrt2)} + c_2e ^{t(3-2\sqrt2)}\]

and my initial value is y(2)=1

Answer 1

so i input that and ive got \[1=c_1e ^{6+4\sqrt2}+c_2e ^{6-4\sqrt2}\]

my question is how do I solve for c_1 or c_2 now? Is there an algebra trick I can use on the not-quite identical powers of e?