Determine order and degree (if defined) of differential equations…

Question 7 of 96beginner💡 UnderstandVery Short1 mark

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

y'' + 2y'' + y' = 0

Correct Answer

Order = 3, Degree = 1

Exercise: EXERCISE 9.1 | Q: 7 | (Page 4)

For More Understanding

Explanation

The highest order derivative present in the equation $y''' + 2y'' + y' = 0$ is $y'''$ , which is the third-order derivative. Thus, the order is 3. The equation is a polynomial in its derivatives, and the highest power of the highest order derivative is 1, making the degree 1.

Solution Steps

Step 1: Identify the highest order derivative in the equation $y''' + 2y'' + y' = 0$ . The term with the highest derivative is $y'''$ .
Step 2: Determine the order. The derivative $y'''$ is the third-order derivative. Therefore, the order is 3.
Step 3: Check if the equation is a polynomial in derivatives. The equation involves derivatives with integer powers, so it is a polynomial equation.
Step 4: Determine the degree. The highest power of the highest order derivative ( $y'''$ ) is 1. Thus, the degree is 1.

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