MathematicsChapter 4: Differential Equations
Common Errors and Solution Checks
Do not divide by a variable expression before checking whether it gives a lost equilibrium solution.
Learning objectives
- State the rule for common errors and solution checks.
- Solve a common errors and solution checks problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Do not divide by a variable expression before checking whether it gives a lost equilibrium solution.
Formula
y=0 and y
Where / symbols
- Common errors and solution checks
- Do not divide by a variable expression before checking whether it gives a lost equilibrium solution.
CONCEPT AND RULE
Do not divide by a variable expression before checking whether it gives a lost equilibrium solution.
METHOD
For common errors and solution checks, 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
Dividing y'=y(1-y) by y(1-y) can lose y=0 and y=1.
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 common errors and solution checks
- 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:
- Dividing y'=y(1-y) by y(1-y) can lose y=0 and y=1.
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
- Common errors and solution checks
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Common Errors and Solution Checks
Sticky Notes · Formula and Worked Revision
Core Idea
- Do not divide by a variable expression before checking whether it gives a lost equilibrium solution.
Rule / Formula
- Do not divide by a variable expression before checking whether it gives a lost equilibrium solution.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- Dividing y'=y(1-y) by y(1-y) can lose y=0 and y=1.
Common Error
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
FBISE Exam Tip
- Show the formula, substitutions, algebra, restrictions, and final answer; method marks need visible reasoning.
60-second revision
- Do not divide by a variable expression before checking whether it gives a lost equilibrium solution.
- Worked pattern: Dividing y'=y(1-y) by y(1-y) can lose y=0 and y=1.
- Final check: domain, sign, notation, units, and reasonableness.
Did you understand this topic?
Your answer is saved with your learning record. It does not mark the topic as mastered.