Consider the differential equation y'''-3y'+2y=0 with initial condition y(1)=5.

Is y=Cx^3 a solution? (Yes/No) If so, find C.

I know that Cx^3 isn't a solution but could you please provide the work for it?

I did...

y'=x^3

y''=0

y'''=0

and then I did

0-3(0)+2(0)=0

Is Cx^3 not a solution because y(1)=5?

I'm a little confused...