Assume that the Fourier sine series representation of is.Which of the following is the unique solution of the one dimensional heat equation on coupled with homogenous Dirichlet boundary conditions and initial condition?

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Assume that the Fourier sine series representation of<br><img src='https://www.fatskills.com/images2/GradExams/203085BB-4CDE-402E-A5EC-575C34B85EBF.png' height='18' width='10'/> is<br><img src='https://www.fatskills.com/images2/GradExams/EE66C1EF-619A-414D-953F-310DC58C9395.png' height='21' width='121'/>.Which of the following is the unique solution of the one dimensional heat equation<br><img src='https://www.fatskills.com/images2/GradExams/250820DE-BEC1-4CA8-996B-09EDB0F045B5.png' height='22' width='84'/> on<br><img src='https://www.fatskills.com/images2/GradExams/97EE8761-9916-48E8-9864-EF8FD459199F.png' height='20' width='42'/> coupled with homogenous Dirichlet boundary conditions<br><img src='https://www.fatskills.com/images2/GradExams/BA16EB1B-364F-4F04-9C45-28FECEBA9433.png' height='20' width='219'/> and initial condition<br><img src='https://www.fatskills.com/images2/GradExams/B7DCFD7A-77C7-4A4D-8CDA-9F8C152C73AA.png' height='20' width='214'/>?





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