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DIFFERENTIAL EQUATIONS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDIFFERENTIAL EQUATIONS1 Mark
Question
Determine order and degree (if defined) of differential equations given in Exercise.
$\bigg(\frac{\text{ds}}{\text{dt}}\bigg)^4 + 3\text{s} \frac{\text{d}^2\text{s}}{\text{dt}^2} =0$
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Answer

The given differential equation is
$\bigg(\frac{\text{ds}}{\text{dt}}\bigg)^4 + 3\text{s} \frac{\text{d}^2\text{s}}{\text{dt}^2} =0$
The highest order derivative present in the differential equation is $\frac{\text{d}^2\text{s}}{\text{dt}^2}$
$\therefore$ its order is 2
The highest power raised to $\frac{\text{d}^2\text{s}}{\text{dt}^2}$ is one, so its degree is 1.

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