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Differential Equations — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations1 Mark
Question
Write the degree of the differential equation $\frac{\text{d}^{2}\text{y}}{\text{dx}^2}+\text{x}\Big(\frac{\text{dy}}{\text{dx}}\Big)^{2}=2\text{x}^{2}\log\Big(\frac{\text{d}^{2}\text{y}}{\text{dx}^2}\Big).$
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Answer

We have,
$\frac{\text{d}^{2}\text{y}}{\text{dx}^2}+\text{x}\Big(\frac{\text{dy}}{\text{dx}}\Big)^{2}=2\text{x}^{2}\log\Big(\frac{\text{d}^{2}\text{y}}{\text{dx}^2}\Big)$
$\frac{\text{d}^{2}\text{y}}{\text{dx}^2}+\text{x}\Big(\frac{\text{dy}}{\text{dx}}\Big)^{2}=2\text{x}^{2}\log\Big(\frac{\text{d}^{2}\text{y}}{\text{dx}^2}\Big)=0$
Here, we observe that LHS of the differential equation be as a polynomial in $\frac{\text{dy}}{\text{dx}}.$
So, its degree is not defined.

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