(4 pts) Let I gt; 0 be a nite number. Use the previous problem to separate variables and solve u; =um+u, t) D, m E (0,1), subject to the boundary...

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4. (4 pts) Let I > 0 be a finite number. Use the previous problem to separate variables and solveu; =um+u, t) D, m E (0,1),subject to the boundary conditionsumlm=0 : 0: u|m=1 : 01 and the initial conditionult=o : 915(33)- Write your solution in the series form. Express the coefficients of the series in terms of gb and (-, -)L2, you do not have tocompute the integrals.