Lesson 480 of 1524
Introduction to Differential Equations
A differential equation coupled with an initial value is called an initial-value problem.
Practice this chapterA differential equation coupled with an initial value is called an initial-value problem. To solve an initial-value problem, first find the general solution to the differential equation, then determine the value of the constant.
A direction field is a mathematical object used to graphically represent solutions to a first-order differential equation Euler’s Method is a numerical technique that can be used to approximate solutions to a differential equation
differential equation — an equation involving a function y = y ( x ) and one or more of its derivatives. solution — a function y = f ( x ) that satisfies the differential equation when f and its derivatives are substituted into the equation. direction field — a mathematical object used to graphically represent solutions to a first-order differential equation. order of a differential equation — the highest order of any derivative of the unknown function that appears in the equation.
Worked example
What does “differential equation” mean in Introduction to Differential Equations?
- 1Use the wording this chapter gives for differential equation.
- 2The book says: an equation involving a function y = y ( x ) and one or more of its derivatives.
- 3Do not use the meaning of solution. That term means a function y = f ( x ) that satisfies the differential equation when f and its derivatives are substituted into the equation.
Result: an equation involving a function y = y ( x ) and one or more of its derivatives
Why. That is the meaning this chapter gives for differential equation.
Do not swap differential equation and solution. differential equation means an equation involving a function y = y ( x ) and one or more of its derivatives. solution means a function y = f ( x ) that satisfies the differential equation when f and its derivatives are substituted into the equation.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.