Question 4 of 96beginner💡 UnderstandVery Short1 mark

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

(d2ydx2)2+cos⁡(dydx)=0\left(\frac{d^2y}{dx^2}\right)^2 + \cos\left(\frac{dy}{dx}\right) = 0
Correct Answer

Order = 2, Degree = Not defined

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

Explanation

This question tests understanding of order and degree of differential equations. The order is determined by the highest derivative present, while the degree requires the equation to be a polynomial in derivatives. The presence of cos(dy/dx) makes it non-polynomial, similar to Example 1(iii) in the textbook where eye^{y}' makes the degree undefined.

Solution Steps

  1. Step 1: Identify the highest order derivative present. The equation contains d2ydx2\frac{d^2y}{dx^2} (second order) and dydx\frac{dy}{dx} (first order). The highest order derivative is d2ydx2\frac{d^2y}{dx^2}, so Order = 2.

  2. Step 2: Check if the equation is a polynomial in derivatives. The term cos⁡(dydx)\cos\left(\frac{dy}{dx}\right) is a trigonometric function of the derivative dydx\frac{dy}{dx}, not a polynomial term.

  3. Step 3: Since the differential equation is not a polynomial equation in its derivatives, the Degree is not defined.

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