00:01
So we'll start with this problem by substituting out the y double prime terms and the other y terms in this equation.
00:06
So we'll have that r squared minus 2r plus 1 equals to 0.
00:13
Or this simplifies down to r minus 1 squared equals to 0.
00:20
And so we have repeating roots of r equals to 1.
00:30
And with this, we can actually build our homogenous solution.
00:33
So our homogenous solution is going to be to form c1, e to the x, plus c2x, e to the x.
00:43
And we have this x term right here because it's repeating.
00:49
And so now we can actually take a stab at the guess for the particular solution.
00:53
So our guess for the particular solution is going to be up to form ax squared plus bx plus c.
00:59
And we have to take the derivative of this twice...
