Determine the general solution to y\'\'\'-5y\'\'+8y\'-4y=0 byconverting to a fir

Question

Determine the general solution to y'''-5y''+8y'-4y=0 byconverting to a first order system of linear differentialequations. I already created the matrix and started to diagonalize, but Irealized that I got a multiplicity and amd I'm pretty sure thatthat makes it undiagonalizable anybody know the next step after Iget the matrix Sorry don't know how to do a proper matrix on this site Please give me a response before 5:30 Pacific Time It Willliterally SAVE MY LIFE!!! Determine the general solution to y''' - 5y''+8y' - 4y=0 byconverting to a first order system of linear differentialequations. I already created the matrix and started to diagonalize, but Irealized that I got a multiplicity and amd I'm pretty sure thatthat makes it undiagonalizable anybody know the next step after Iget the matrix

Explanation / Answer

First change the equation so you can find your "zeros". x3-5x2+8x-4=0, x=1 and (x-2)2 , which means you have arepeat of x=2. With that, the general soln is: y=C1ex+C2e2x+C3xe2x The repeated root has to have the x added. I forget why, butthat is what I remember as a rule. You don't need a matrix to solvethis. I hope this helps The repeated root has to have the x added. I forget why, butthat is what I remember as a rule. You don't need a matrix to solvethis. I hope this helps

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