<prompt> Onyesha kuwa utheta, phiY_11theta, phi iliyotolewa katika Mfano E-2 inatosheleza mlinganyo nabla2 ufraccr2 u , ambapo c ni ya kudumu. Thamani ya c ni nini?  <response>: Kwa sababu utheta, phi haitegemei r, tunaanza nayonabla2 ufrac1r2 sin theta fracpartialpartial thetaleftsin theta fracpartial upartial thetakuliafrac1r2 sin 2 theta fracpartial2 upartial phi2Kubadilishautheta, phi-kushotofrac38 pikulia1 2 ei phi sin thetandani ya nabla2 u inatoaanzailiyopangwanabla2 u -kushotofrac38 pikulia1 2kushotofracei phir2 sin thetakushotocos 2 theta-sin 2 thetakulia-fracsin thetar2 sin 2 theta ei phi haki -kushotofrac38 pikulia1 2 fracei phir2kushotofrac1-2 sin 2 thetasin theta-frac1sin thetakulia 2kushotofrac38 pikulia1 2 fracei phi sin thetar2mwishoiliyopangwaau c-2. 