MathematicsChapter 4: Differential Equations

Using An Integrating Factor

Multiply every term by the factor, recognize a product derivative, integrate, and divide.

Learning objectives

State the rule for using an integrating factor.
Solve a using an integrating factor problem step by step.
Check the result, restrictions, notation, and units.

Definition

Multiply every term by the factor, recognize a product derivative, integrate, and divide.

Formula

y=e^x/2+Ce⁽-x).

Where / symbols

Using an integrating factor: Multiply every term by the factor, recognize a product derivative, integrate, and divide.

CONCEPT AND RULE

Multiply every term by the factor, recognize a product derivative, integrate, and divide.

METHOD

For using an integrating factor, identify the given information and required result. Select the matching definition or formula, state its conditions, substitute carefully, simplify one line at a time, and check.

WORKED EXAMPLE

Solving gives y=e^x/2+Ce⁽-x).

COMMON MISTAKE

Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.

How to solve using an integrating factor

Identify the mathematical objects, givens, restrictions, and required result.
Choose and write the relevant definition, theorem, or formula.
Substitute with brackets and carry out one justified step per line.
Simplify, state the final answer clearly, and verify it in the original setting.

Worked example

Worked example:
Solving gives y=e^x/2+Ce⁽-x).

In simple words

Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.

Key points

Using an integrating factor
rule
worked example

Exam preparation

Exam Focus

Quick revision

Revision Zone

Review the key facts, formulas and checks before you move on.