Question
Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\frac{\text{d}^2\text{y}}{\text{dx}^2}+\Big(\frac{\text{dy}}{\text{dx}}\Big)^2+\text{xy}=0$

Answer

$\frac{\text{d}^2\text{y}}{\text{dx}^2}+\Big(\frac{\text{dy}}{\text{dx}}\Big)^2+\text{xy}=0$
In this differential equation, the order of the highest order derivative is 2 and its power is 1. So, it is a differential equation of order 2 and degree 1.
It is a non-linear differential equation, as the differential coefficient $\frac{\text{dy}}{\text{dx}}$ has exponent 2, which is greater than 1.

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