Question 1 of 96beginner💡 UnderstandVery Short1 mark

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

d4ydx4+sin⁡(y′′)=0\frac{d^4y}{dx^4} + \sin(y'') = 0
Correct Answer

Order = 4

Degree = Not defined

Exercise: EXERCISE 9.1 | Q: 1 | (Page 4)
For More Understanding

Explanation

The highest order derivative present in the given differential equation is d⁴y/dx⁴, which is of order 4. Therefore, the order is 4. For the degree to be defined, the differential equation must be a polynomial equation in its derivatives. However, the term sin(y'') is a trigonometric function of the derivative y'', making the equation not a polynomial in derivatives. Hence, the degree is not defined.

Solution Steps

  1. Step 1: Identify the highest order derivative: d⁴y/dx⁴ (order 4)

  2. Step 2: Order = 4

  3. Step 3: Check if the equation is a polynomial in derivatives: The term sin(y'') is not polynomial

  4. Step 4: Degree is not defined

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