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**i_zz_y_ill** par (iv) (B)* im stuck on, pls bare with me

q1 A solution is sought to te differential eqn

y(doubledot)+4(dot)+4y=2e^-2t

(i)find the complementary function

(ii)Explain why an expression of either of the fomrs ae^-2t or ate^-2t cannot be a particular integral of the D.e. State a correct form for the partcular integral and hence show the the general solution is:

y=(A+Bt+t^2)e^-2t

(iii)It is given that y=0 when t=1 and that y=0 when t=3. Calculate the constants A and B and write the particular solution in factorised form.

(iv)By reference to the previous answer, write dwn the particular solution in the cases

(A) y=0 when t=2 and y=0 when t=7

(B)*y=0 only when t=1

the answer in (iii) was (t-1)(t-3)e^-2t

I can't really see how this relates to (B).

I just put in y=0 and t=1 getting A+B+1=0 in which case A and B can be anything adding up to -1. The mark scheme i have however gives a mark for the answer being y=e^-2t(t-1)^2 in which case I manipulated this aswer and found that A would equal 1 and B would equal -2.(which contradicts what i thought) Obviously I am missing something either from 3 or something fundamental or this Question is very badly worded or ultimately wrong. Any inputs would be highly appreciated thanks!