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DIFFERENTIAL EQUATIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDIFFERENTIAL EQUATIONS1 Mark
Question
For each of the differential equations given below, indicate its order and degree (if defined).
$\frac{\text{d}^2\text{y}}{\text{dx}^2}+5\text{x}\Big(\frac{\text{dy}}{\text{dx}}\Big)^2-6\text{y}=\log\text{x}$
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Answer

Given: Differential equation $\frac{\text{d}^2\text{y}}{\text{dx}^2}+5\text{x}\Big(\frac{\text{dy}}{\text{dx}}\Big)^2-6\text{y}=\log\text{x}$
The highest order derivative present in this differential equation is $\frac{​​\text{d}^2\text{y}}{\text{dx}^2}$ and hence order of this differential equation if 2.
The given differential equation is a polynomial equation in derivatives and highest power of the highest order derivative $\frac{​​\text{d}^2\text{y}}{\text{dx}^2}$ is 1.
Therefore, Order = 2, Degree = 1

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