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Question Number 51494 by Tawa1 last updated on 27/Dec/18

$$\mathrm{Solve}:({\mathrm{t}}^2+1)\frac{\mathrm{dp}}{\mathrm{dt}}={\mathrm{p}}^{\mathrm{t}}$$

Commented by tanmay.chaudhury50@gmail.com last updated on 27/Dec/18

$$(t^2+1)\frac{d^{2}p}{{dt}^2}+\frac{dp}{dt}\times 2t=\frac{d}{dt}\left(p^t\right)$$$$y=p^t$$$$lny=tlnp$$$$\frac{1}{y}\frac{dy}{dt}=\frac{t}{p}\frac{dp}{dt}+lnp$$$$\frac{dy}{dt}=y[\frac{t}{p}\frac{dp}{dt}+lnp]$$$$uniquequestion...forcethesleepingcellofbrain$$$$towakeup...searchingwaytosolve...$$

Commented by Tawa1 last updated on 27/Dec/18

$$\mathrm{I}\mathrm{will}\mathrm{wait}\mathrm{sir},\mathrm{thanks}\mathrm{for}\mathrm{your}\mathrm{time}.\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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