Consider the partial differential equation u at' vith boundary conditions u(0, t) = 0 and u(7, t) = 0 for t > 0, and the initial condition (z,0) = = (-2 + }=). The general solution that satisfies the boundary conditions is u(x, t) = Ane-9n²t sin(3næ). n=1 Select the option that gives the correct method for determining the constants A, from the given nitial condition. Select one: 3 An (-a+ ) | sin(3næ) dz 6 An z (-2+r) cos(3nz) dz = - 0. 3 An = 을 (-z+") coe(3na) da 6 An * (-x+) sin(3nz) dæ +=-)= An z(-z+ 찌) sin(3nz) dz

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