Question 2 of 96beginner💡 UnderstandVery Short1 mark

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

y′+5y=0y' + 5y = 0
Correct Answer

Order = 1, Degree = 1

Exercise: EXERCISE 9.1 | Q: 2 | (Page 4)
For More Understanding

Explanation

The differential equation y' + 5y = 0 contains only the first derivative y' = dy/dx. Since the highest order derivative present is dy/dx (first order), the order is 1. The equation is a polynomial equation in y' with the highest power raised to dy/dx being one, so the degree is also 1.

Solution Steps

  1. Step 1: Identify the highest order derivative present in y' + 5y = 0. The only derivative is y' = dy/dx, which is a first-order derivative. Hence, Order = 1.

  2. Step 2: Check if the equation is a polynomial in derivatives. The equation y' + 5y = 0 is polynomial in y' with the highest power of y' being 1. Hence, Degree = 1.

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