Question 3 of 96beginner💡 UnderstandVery Short1 mark

Determine order and degree (if defined) of differential equations given in Exercises 1 to 10.

(dsdt)4+3sd2sdt2=0\left(\frac{ds}{dt}\right)^4 + 3s \frac{d^2s}{dt^2} = 0
Correct Answer

Order = 2, Degree = 1

Exercise: EXERCISE 9.1 | Q: 3 | (Page 4)
For More Understanding

Explanation

The question asks to find the order and degree of the differential equation from Exercise 9.1, Question 3. According to the textbook context, order is determined by the highest order derivative present, and degree is the highest power of the highest order derivative when the equation is a polynomial in derivatives.

Solution Steps

  1. Step 1: Identify the highest order derivative. The equation contains dsdt\frac{ds}{dt} (first order) and d2sdt2\frac{d^2s}{dt^2} (second order). The highest order derivative is d2sdt2\frac{d^2s}{dt^2}, so Order = 2.

  2. Step 2: Check if the equation is a polynomial in derivatives. The equation (dsdt)4+3sd2sdt2=0\left(\frac{ds}{dt}\right)^4 + 3s \frac{d^2s}{dt^2} = 0 is a polynomial equation in derivatives with positive integer powers.

  3. Step 3: Find the highest power of the highest order derivative. The highest order derivative d2sdt2\frac{d^2s}{dt^2} appears with power 1. Therefore, Degree = 1.

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