Topic 4 - Differential Equations
We have below bronze, silver, gold and platinum tutorials for our Advanced Higher Maths Differential Equations topic. Typically as you work through the modules, the difficulty of the skills increase by one step ensuring smooth progression. Simply click on the video to play it and pause it at the relevant points for you to attempt your practice question. Each tutorial has a corresponding worksheet for you to download for additional practice. Make sure you have a pen and paper handy! Be sure to mark your work for every exercise attempted. Good luck!
Essential prior knowledge:-
Higher Maths
Contents:-
4.1 - Seperable first order differential equations
4.2 - Second order homogenous differential equations
4.3 - Second order non-homogenous differential equations
4.1: Seperable first order differential equations
Outcome 1 - Bronze Level
Video 49: Seperable first order differential equations. In this video we learn how to find general and particular solutions for first order differential equations of the form f(y)dy = g(x)dx.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [117.1 KB]
Outcome 2 - Silver Level
Video 50: Seperable first order differential equations. In this video we learn how to deal with seperable first order differential equations using our knowledge of logs and exponentials.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [133.5 KB]
Outcome 3 - Gold Level
Video 51: Seperable first order differential equations using the integrating factor. In this video we learn how to solve seperable first order differential equations of the form dy/dx + P(x)y = Q(x) by first calculating the integrating factor.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [112.5 KB]
4.2: Second order homogenous differential equations
Outcome 1 - Bronze Level
Video 52: Second order homogenous differential equations - with real and distinct roots. In this video we learn how to find particular solutions for second order homogenous differential equations with real and distinct roots.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [128.3 KB]
Outcome 2 - Silver Level
Video 53: Second order homogenous differential equations - with real and equal roots. In this video we learn how to find particular solutions for second order homogenous differential equations with real and equal roots. Another General Solution formula must be learned!
Now you've watched the video, try these practice questions.
Adobe Acrobat document [130.2 KB]
Outcome 3 - Gold Level
Video 54: Second order homogenous differential equations - with no real roots. In this video we learn how to find particular solutions for second order homogenous differential equations with no real roots. Prior knowledge of the quadratic formula is essential here.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [142.6 KB]
SQA Exam Questions
You will find below a collection of second order homogenous differential equations SQA past paper questions. You should click on a question, pause the video when instructed and give the question your best shot. Then un-pause the video and watch the worked solution. You should make this section a regular place to come back to when revising. Even if you get the correct answer, it is recommended that you try all these questions more than once at various stages throughout the year.
4.2 - Second order homegeonous differential equations
Alternatively you can click here to view all the questions on a playlist.
4.3: Second order non-homogenous differential equations
Outcome 1 - Bronze Level
Video 55: Second order non-homogenous differential equations - with linear or quadratic RHSs. In this video we learn how to find general solutions for second order non-homogenous differential equations with a linear or quadratic function as the right hand side.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [130.9 KB]
Outcome 2 - Silver Level
Video 56: Second order non-homogenous differential equations - with exponential RHSs. In this video we learn how to find general solutions for second order non-homogenous differential equations with an exponential function as the right hand side.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [128.6 KB]
Outcome 3 - Gold Level
Video 57: Second order non-homogenous differential equations - with trigonometric RHSs. In this video we learn how to find general solutions for second order non-homogenous differential equations with a trigonometric function as the right hand side.
Now you've watched the video, try these practice questions.
Adobe Acrobat document [135.9 KB]
SQA Exam Questions
You will find below a collection of second order non homogenous differential equations SQA past paper questions. You should click on a question, pause the video when instructed and give the question your best shot. Then un-pause the video and watch the worked solution. You should make this section a regular place to come back to when revising. Even if you get the correct answer, it is recommended that you try all these questions more than once at various stages throughout the year.
4.3 - Second order non homegeonous differential equations
- 2022 Question 15
- 2021 Question 15
- 2017 Question 14
- 2016 Question 15
- 2015 Question 16
- 2013 Question 14
- 2011 Question 14
- 2008 Question 13
- 2007 Question 8
- 2005 Question 14
- 2003 Question B6
- 2002 Question B5
Alternatively you can click here to view all the questions on a playlist.
Congratulations!
You have completed this module - well done! Remember to go back and redo any areas of weakness, that's how we improve. If you are happy with all areas, go back to the main menu and pick another topic to practice!
Calling all Parents & Students!
Click here for more information regarding access to our online learning portals to aid home revision.
Print 