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Q.
If $p$ and $q$ are the order and degree of the differential equation $y \frac{ dy }{ dx }+ x ^{3} \frac{ d ^{2} y }{ dx ^{2}}+ xy =\cos x$, then
Differential Equations
Solution:
The given differential equation is
$y \frac{d y}{d x}+x^{3} \frac{d^{2} y}{d x^{2}}+x y=\cos x$
Its order is 2 and its degree is 1 .
$\therefore p =2$ and $q =1$
Hence, $p > q$