Prior content: A2 Integration (See Separating the Variables),
Previous Section: Hyperbolic Functions
Next Section: Modelling with Differential Equations
Contents
- Whole Topic Notes
- 7A Part 1 First Order Differential Equations 2.0
- 7A Part 2 First Order Differential Equations and Integrating Factors
- 7B Homogeneous Second Order Differential Equations
- 7C Particular Integrals of Second Order Differential Equations
- 7D Finding Constants of Second Order Differential Equations
- Whole Topic Summary Resources (Including Past Paper Questions)
Whole Topic Notes
Download Full Topic Slides
- Textbook Notes as PPTs (Courtesy of Owen134866)
Full Notes to Accompany Slides
Dr Frost
- Dr Frost A2 Core Pure Methods in Differential Equations Section
- Dr Frost A2 Core Pure Methods in Differential Equations Slides
- Blank Notes to Follow Slides Word Doc or PDF (Courtesy of King’s Chester Maths Department)
Acute Learning Whole Chapter Problem Pairs
Notes
- Physics & Maths Tutor
- CP2 Ch.7 Methods in Differential Equations: Cheat sheet
7A Part 1 First Order Differential Equations 2.0
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths (Up to 7:07)
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 622c: Determine general solutions to differential equations involving general polynomial expressions in x and y, including roots and reciprocals
- 622d: Determine particular solutions to differential equations involving general polynomial expressions in x and y, including roots and reciprocals
- 738a: Solve a first order differential equation where the left-hand-side of the equation can be expressed as d/dx≤ft[f(x)yright] (not yet active)
- 622: Exam Practice: Solving linearly separable first order differential equations
- 738: Exam Practice: Using integrating factors to solve differential equations given in the form dy/dx + P(x)y = Q(x)
Other resources
3Blue1Brown Linear transformations and matrices | Chapter 3, Essence of linear algebra
Enrichment Video
3Blue1Brown: Differential equations, a tourist's guide
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Online Platform
- Bossmaths interactive 2×2 transformations and questions
7A Part 2 First Order Differential Equations and Integrating Factors
Textbook resources
Dr Frost resources
Other resources
Worksheets
- Mathshelper (Jon Stone)
- MadAsMaths (T. Madas)
- First Order Differential Equations Exam Questions Q1–9, 11–20, 22, 24–28 (difficulty 2–5 of 5)
- First Order Differential Equations Practice Q1–6
- Hyperbolic Functions Q12 (difficulty 2 of 5)
- First Order Differential Equations Exam Questions Q10 (difficulty 3 of 5)
- Hyperbolic Functions Q16 (difficulty 3 of 5)
Online Platforms
- Khan Academy
- Separable differential equations: Videos & practice
7B Homogeneous Second Order Differential Equations
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 739a: Determine the general solution of a differential equation a d2y/dx2 + b dy/dx + cy = 0 where the auxiliary equation has distinct roots. (not yet active)
- 739b: Determine the general solution of a differential equation a d2y/dx2 + b dy/dx + cy = 0 where the auxiliary equation has equal roots. (not yet active)
- 739c: Determine the general solution of a differential equation a d2y/dx2 + cy = 0 where the auxiliary equation has imaginary roots. (not yet active)
- 739d: Determine the general solution of a differential equation a d2y/dx2 + b dy/dx + cy = 0 where the auxiliary equation has complex roots. (not yet active)
- 739f: Determine the general solution to a homogeneous second order differential equation involving hyperbolic terms. (not yet active)
- 739: Exam Practice: Homogeneous second order differential equations
Other resources
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Online Platform
- Bossmaths interactive 2×2 transformations and questions
Activities
- Ben Sparks (GeoGebra)
- Second Order Linear Differential Equation Solver: GeoGebra
Online Platforms
- Khan Academy
- Second order linear homogeneous equations: Videos & practice
- Complex roots of the auxiliary equation: Videos & practice
Worksheets
- MadAsMaths (T. Madas)
- Second Order Differential Equations Exam Questions Basic Questions Q1 (difficulty 2 of 5)
- Second Order Differential Equations Practice Practice Q1–2
7C Particular Integrals of Second Order Differential Equations
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Questions
- Dr Frost Questions (very short)
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 740a: Determine the general solution of a second order differential equations given in the form a d2y/dx2 + b dy/dx + cy = k (not yet active)
- 740b: Determine the general solution of a second order differential equations given in the form a d2y/dx2 + b dy/dx + cy = px + q (not yet active)
- 740c: Determine the general solution of a second order differential equations given in the form a d2y/dx2 + b dy/dx + cy = px2 + qx + r (not yet active)
- 740d: Determine the general solution of a second order differential equations given in the form a d2y/dx2 + b dy/dx + cy = peqx (not yet active)
- 740e: Determine the general solution of a second order differential equations given in the form a d2y/dx2 + b dy/dx + cy = k sin omega x (not yet active)
- 740f: Determine the general solution of a non-homogeneous second order differential equation where the particular integral overlaps with the complementary function. (not yet active)
- 740h: Determine general solutions to non-homogenous second order differential equations in a modelled context. (not yet active)
- 740: Exam Practice: Non-homogeneous second order differential equations
Other resources
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Online Platform
- Bossmaths interactive 3×3 transformations and questions
Online Platforms
- Khan Academy
- Method of undetermined coefficients: Videos & practice
Worksheets
- MadAsMaths (T. Madas)
- Second Order Differential Equations Exam Questions Basic Questions Q2–3, 6–7; Standard Questions Q2, 13 (difficulty 2–4 of 5)
- Second Order Differential Equations Practice Practice Q3–5, 10–12
7D Finding Constants of Second Order Differential Equations
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 739e: Determine the particular solution of a homogeneous second order differential equation. (not yet active)
- 739g: Determine the general solution of a homogeneous second order differential equation in a modelled context. (not yet active)
- 739h: Comment on the suitability of the solution to a second order differential equation which in a modelled context. (not yet active)
- 740g: Determine the particular solution to a non-homogeneous second order differential equation. (not yet active)
- 740i: Determine particular solutions to non-homogenous second order differential equations in a modelled context and find the output for a given input. (not yet active)
- 739: Exam Practice: Homogeneous second order differential equations
- 740: Exam Practice: Non-homogeneous second order differential equations
Other resources
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Online Platform
- Bossmaths interactive 2×2 transformations and questions
Worksheet & Activities
- MEI activities from old FP1
Worksheets
- MadAsMaths (T. Madas)
- Second Order Differential Equations Exam Questions Basic Questions Q4–5, 8; Standard Questions Q1, 3–7, 12, 14–16; Hard Question Q1 (difficulty 3–4 of 5)
- Second Order Differential Equations Practice Practice Q6–12
Whole Topic Summary Resources (Including Past Paper Questions)
External whole topic past paper style questions
- WW Dr Frost Style QQQs (Version 1) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
- WW Dr Frost Style QQQs (Version 2) Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)
- Advanced Highers Matrices Exam Questions & Answers
Activities
- NRICH (student problems)
Worksheets
- Jethwa Maths
- 10 Minute Starters: Methods in Differential Equations
- Physics & Maths Tutor
- CP2 Ch.7 Methods in Differential Equations: Questions by topic