Question 6 of 96beginner💡 UnderstandVery Short1 mark

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

(y′′)2+(y′′)3+(y′)4+y5=0(y'')^2 + (y'')^3 + (y')^4 + y^5 = 0
Correct Answer

Order = 2, Degree = 3

Exercise: EXERCISE 9.1 | Q: 6 | (Page 4)
For More Understanding

Explanation

The highest order derivative present in the given differential equation 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 3, as seen in the term (y'')³. Therefore, the degree is 3.

Solution Steps

  1. Step 1: Identify the highest order derivative present → y'' (second derivative) → Order = 2

  2. Step 2: Check if the equation is a polynomial in derivatives → Yes, all terms are polynomial in y'', y', and y

  3. Step 3: Find the highest power of the highest order derivative (y'') → The term (y'')³ has power 3 → Degree = 3

PreviousNext