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Differential Equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations1 Mark
MCQ
The degree of the differntial equation $\left\{5+\Big(\frac{\text{dy}}{\text{dx}}\Big)^{2}\right\}^{\frac{5}{3}}=\text{x}^{5}\Big(\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}\Big)$ is:
  • A
    4
  • ✓
    3
  • C
    5
  • D
    10
✓

Answer

Correct option: B.
3
Solution:
We have,
$\left\{5+\Big(\frac{\text{dy}}{\text{dx}}\Big)^{2}\right\}^{\frac{5}{3}}=\text{x}^{5}\Big(\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}\Big)$
Taking cube power on both sides, we get
$\left\{5+\Big(\frac{\text{dy}}{\text{dx}}\Big)^{2}\right\}^{5}=\text{x}^{15}\Big(\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}\Big)^{3}$
The highest order derivative is $\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}$ and its power is 3.
Hence, the degree is 3.
 

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