Question 9 of 96beginner💡 UnderstandVery Short1 mark

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

y′′+(y′)2+2y=0y'' + (y')^2 + 2y = 0
Correct Answer

Order = 2, Degree = 1

Exercise: EXERCISE 9.1 | Q: 9 | (Page 4)
For More Understanding

Explanation

The differential equation is y'' + (y')² + 2y = 0. The highest order derivative present is y'' (second derivative), so the order is 2. The equation is a polynomial equation in derivatives y'' and y'. The highest power of the highest order derivative y'' is 1, so the degree is 1.

Solution Steps

  1. Step 1: Identify the highest order derivative present in the equation. The equation contains y'' and y'. The highest order derivative is y'' (second derivative), so Order = 2.

  2. Step 2: Check if the equation is a polynomial in derivatives. The equation y'' + (y')² + 2y = 0 is a polynomial in y'' and y' (no transcendental functions of derivatives).

  3. Step 3: Find the highest power of the highest order derivative. The highest order derivative y'' has power 1. Therefore, Degree = 1.

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