Introduction to Differential Equations
This worksheet introduces fundamental concepts of differential equations, including order, linearity, and verification of solutions, suitable for Grade 9 math students.
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Introduction to Differential Equations
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
What is a Differential Equation?
A differential equation is an equation that relates one or more functions and their derivatives. It describes how a quantity changes over time or space.
1. A differential equation involves a function and its .
2. The of a differential equation is the highest order of the derivative present in the equation.
3. A differential equation is called if the dependent variable and its derivatives appear only in the first power and are not multiplied together.
4. Which of the following is an example of a differential equation?
2x + 3 = 7
dy/dx = 5x
y = x^2 + 3
x^2 + y^2 = 25
5. What is the order of the differential equation d^2y/dx^2 + 3(dy/dx) - 2y = 0?
0
1
2
3
6. The differential equation dy/dx = y^2 is a linear differential equation.
True
False
7. Verify that y = e^(2x) is a solution to the differential equation dy/dx = 2y.
8. Give an example of a first-order, non-linear differential equation.