Second order equations and first order equations solved with an integrating factor. The solution splits into a complementary function and a particular integral.
Syllabus points covered
- Find and use an integrating factor to solve a first order linear differential equation
- Solve second order linear equations with constant coefficients, finding the complementary function
- Find a particular integral for standard forms of the right-hand side
- Use substitutions to reduce an equation to a standard form and interpret solutions in context
Common mistakes
- Omitting the particular integral and giving only the complementary function.
- Choosing a particular integral of the same form as part of the complementary function without multiplying by x.
- Forgetting to multiply the whole equation by the integrating factor, not just one side.
- Applying initial conditions to the complementary function before adding the particular integral.
Worksheets
Use these as soon as you've learned the topic and need to practise it. Start with the worksheet, check yourself against the answers, and only then look at the step-by-step solutions.
- Practice worksheetComing soon
- Worksheet answersComing soon
- Step-by-step solutionsComing soon
Topical past papers
Move on to these once you've worked through the worksheets and are ready for harder, exam-style questions. Real past-paper questions on this topic, with the official mark scheme and full worked solutions.
- Topical questions
- Mark scheme
- Step-by-step worked solutionsComing soon
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