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- Homework Statement
- ##y^{'''} - 6y^{''} +12y^{'} - 8 y=0##

- Relevant Equations
- Let the solution be ##y = e^{mx}##. Then, the characteristic equation is:

## m^3 -6m^2 + 12m -8 = 0##

The characteristic equation ## m^3 -6m^2 + 12m -8 = 0## has just one single, I mean all three are equal, root ##m=2##. So, one of the particular solution is ##y_1 = e^{2x}##. How can we find the other two? The technique ##y_2 = u(x) e^{2x}## doesn't seem to work, and even if it were to work how would have we got the the third particular solution?