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Differential Equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations1 Mark
Question
Write the degree of the differential equation $\text{a}^{2}\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}=\left\{1+(\frac{\text{dy}}{\text{dx}})^{2}\right\}^{\frac{1}{4}}.$
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Answer

We have,
$\text{a}^{2}\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}=\left\{1+(\frac{\text{dy}}{\text{dx}})^{2}\right\}^{\frac{1}{4}}$
$\left\{\text{a}^{2}\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}\right\}^{4}={1+\big(\frac{\text{dy}}{\text{dx}}\big)^{2}}$
Degree of the diffrential equation is the degree of the highest order derivative.
Therefore, the deree must be 4.

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