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Show that the solutions (Q” + n^2Q = 0) and (r^2W”+rW’+

Show that the solutions (Q” + n^2Q = 0) and (r^2W”+rW’+(k^2r^2-n^2)W = 0) to … Show more Show that the solutions (Q” + n^2Q = 0) and (r^2W”+rW’+(k^2r^2-n^2)W = 0) to (u_{tt} = c^2(u_{rr} + 1/r(u_{r})+ 1/r^2(u_{thetatheta})) satisfying (u(R,theta,t)= 0) are (u^*_{nm}=(A^*_{nm}cos(ck_{nm}t)+B^*_{nm}sin(ck_{nm}t))*J_n(k_{nm}r)sin(ntheta)) and (u_{nm}=(A_{nm}cos(ck_{nm}t)+B_{nm}sin(ck_{nm}t))*J_n(k_{nm}r)cos(ntheta)) • Show less


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