1.2.2. Order and Degree

Try these first

1. 1.

   Identify the order and degree of the equation dy/dx + 2y = 0.

   Hint

   Count the highest derivative and its power.

2. 2.

   What is the order of the equation d^3y/dx^3 + 4y = 5?

   Hint

   Look for the highest derivative present.

3. 3.

   What is the order of the differential equation d^4y/dx^4 + 2y' = 3?

   • 1
   • 4
   • 3

   Hint

   Focus on the maximum derivative to find the order.

4. 4.

   True or False: The degree of a differential equation is the exponent of the highest order derivative.

   • True
   • False

   Hint

   Think about how we define the degree.

5. 5.

   Given the differential equation (d^2y/dx^2)^2 + y' + y = 0, determine both the order and degree. Explain your reasoning.

   Hint

   Identify the main derivative before determining the polynomial nature.

6. 6.

   Create a new example of a differential equation with order 3 but degree 1; explain your choice.

   Hint

   Focus on ensuring the highest derivative is counted and degrees are polynomial.