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Q. If $ p $ and $ q $ are the order and degree of the differential equation $ y\frac{dy}{dx}+x^{3}\left(\frac{d^{2}y}{dx^{2}}\right)^{3}+xy = \cos x $ , then

AMUAMU 2016Differential Equations

Solution:

We have, $y \frac{dy}{dx} + x^3(\frac{d^2y}{dx^2})^3 + xy = \cos\,x$
Order, $p = 2$ and degree, $q = 3$
$\therefore p < q \,\,[\because 2 < 3]$