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Question
If p and q are the order and degree of the differential equation \[y\frac{dy}{dx} + x^3 \frac{d^2 y}{d x^2} + xy\] = cos x, then
Options
p < q
p = q
p > q
none of these
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Solution
p > q
We have,
\[y\frac{dy}{dx} + x^3 \frac{d^2 y}{d x^2} + xy = \cos x\]
\[\text{ The highest order derivative is }\frac{d^2 y}{d^2 x}\text{ and it's degree is 1}\]
So, the order is 2 and the degree is 1.
\[ \therefore p = 2\text{ and }q = 1\]
\[\text{ Clearly, }p > q\]
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