#OK to post homework
#Nicholas DiMarzio,09/13/21, assignment 3
#
#Problem 1
#

solve({y(t)^2 - y(t) = 0, y(0) = 1, D(y)(0) = 0}, y(t));






#Problem 2
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rsolve({a(n - 1)^2 = 0, a(1) = 2^(2^n)}, a(n));
                  /        / n\              \ 
                 {         \2 /               }
                  \a(1) = 2    , a(n - 1) = 0/ 

rsolve({a(n - 1)^2, a(n) = 3*2^(2^n)}, a(n));
                 /          / n\              \ 
                {           \2 /               }
                 \a(n) = 3 2    , a(n - 1) = 0/ 


#Problem 3
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rsolve({a(n) - 3*a(n - 1) + 2*a(n - 2) = 0, a(0) = 2, a(1) = 3}, a(n));
                                  n
                             1 + 2 

#Problem 4
#
rsolve({a(n) - 2*a(n - 1) - 2*a(n - 2) + 2*a(n - 3), a(0) = 3, a(1) = 2, a(2) = 6}, a(n));
Error, (in genfunc:-rgf_expand) unable to compute coeff

#Problem 5
#
rsolve({a(n) - a(n - 4), a(0) = 1, a(1) = 0, a(2) = 0, a(3) = 0}, a(n));
                  1     n   1  n   1     n   1
                  - (-1)  + - I  + - (-I)  + -
                  4         4      4         4