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Differential Equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations1 Mark
Question
Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\sqrt{1-\text{y}^2}\text{dx}+\sqrt{1-\text{x}^2}\text{dx}=0$
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Answer

$\sqrt{1-\text{y}^2}\text{dx}+\sqrt{1-\text{x}^2}\text{dx}=0$

$\Rightarrow\sqrt{1-\text{y}^2}\text{dx}=-\sqrt{1-\text{x}^2}\text{dy}$

$\Rightarrow-\frac{\sqrt{1-\text{y}^2}}{\sqrt{1-\text{x}^2}}=\frac{\text{dy}}{\text{dx}}$

$\Rightarrow\sqrt{1-\text{x}^2}\frac{\text{dy}}{\text{dx}}+\sqrt{1-\text{y}^2}=0$

In this differential equation, the order of the highest order derivative is 1 and its power is 1. So, it is a differential equation of order 1 and degree 1.

Its is a non linear equation, as the exponent of dependent variable(y) is more than 1 (on expanding $\sqrt{1-\text{y}^2}$ binomially).

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