Question

# The degree of the differential equation ${\left(\frac{{d}^{2}y}{d{x}^{2}}\right)}^{3}+{\left(\frac{dy}{dx}\right)}^{2}+\mathrm{sin}\left(\frac{dy}{dx}\right)+1=0$, is (a) 3 (b) 2 (c) 1 (d) not defined

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Solution

## (d) not defined We have, ${\left(\frac{{d}^{2}y}{d{x}^{2}}\right)}^{3}+{\left(\frac{dy}{dx}\right)}^{2}+\mathrm{sin}\left(\frac{dy}{dx}\right)+1=0$ $\mathrm{The}\mathrm{highest}\mathrm{order}\mathrm{derivative}\mathrm{in}\mathrm{this}\mathrm{equation}\mathrm{is}\frac{{d}^{2}y}{{d}^{2}x}.\phantom{\rule{0ex}{0ex}}\mathrm{But}\mathrm{the}\mathrm{equation}\mathrm{cannot}\mathrm{be}\mathrm{expressed}\mathrm{as}\mathrm{a}\mathrm{polynomial}\mathrm{in}\mathrm{differential}\mathrm{coefficient}.\phantom{\rule{0ex}{0ex}}\mathrm{Hence},\mathrm{the}\mathrm{degree}\mathrm{is}\mathrm{not}\mathrm{defined}.$

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