If-t-n-e-r-2-ut-find-the-value-of-n-which-will-make-1-r-2-r-r-2-r-equal-to-t-

Tinku Tara June 4, 2023 None 0 Comments

Question Number 17805 by ibraheem160 last updated on 10/Jul/17

If θ=t^n e^(−r^(2/(ut)) ) ,find the value of n which will make (1/r^2 ) (∂/∂r)(r^2 (∂θ/(∂r))) equal to (∂θ/∂t)

$${If}\:\theta={t}^{{n}} {e}^{−{r}^{\frac{\mathrm{2}}{{ut}}} } ,{find}\:{the}\:{value}\:{of} \\ $$$${n}\:{which}\:{will}\:{make}\:\frac{\mathrm{1}}{{r}^{\mathrm{2}} }\:\frac{\partial}{\partial{r}}\left({r}^{\mathrm{2}} \frac{\partial\theta}{\left.\partial{r}\right)}\right. \\ $$$${equal}\:{to}\:\frac{\partial\theta}{\partial{t}} \\ $$

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