= Solution
{c}
The <Cauchy momentum equation> in <static elastic equilibrium>, with zero <body force>, is $\operatorname{div}\mathbf T=\mathbf0$. The <Cauchy stress tensor> is symmetric. <Material isotropy> and the equal tangential <principal stretches> imply $t_\theta=t_\phi$, so its radial equation is
$$
\boxed{\frac{dt_r}{dr}+\frac2r(t_r-t_\theta)=0,\qquad
\text{equivalently}\quad
\frac{dt_r}{dr}=\frac2r(t_\theta-t_r).}
$$
All <stresses> and spatial derivatives in this equation are measured in the <current configuration>.
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