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This lecture from M.I.T. is 40-50 minutes long delivered by Professor Arthur Mattuck and covers methods of solving differential equations. It is aimed at undergraduate students.

These lectures will give you some idea of how this subject is treated at university level.

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Video from MIT
Free lecture notes, exams, and videos are available from Massachusetts Institute of Technology at MIT. No registration required.

This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA A-Level (UK - Pre-2017)FP32nd Order Differential EquationsXTRA-
AQA A2 Further Maths 2017Pure MathsExtraDifferential Equations Videos-
AQA AS/A2 Further Maths 2017Pure MathsExtraDifferential Equations Videos-
CCEA A-Level (NI)FP22nd Order Differential EquationsXTRA-
Edexcel A-Level (UK - Pre-2017)FP22nd Order Differential EquationsXTRA-
Edexcel A2 Further Maths 2017Core Pure MathsExtra(2nd) Differential Equations - Extra-
Edexcel AS/A2 Further Maths 2017Core Pure MathsExtra(2nd) Differential Equations - Extra-
Methods (UK)M112nd Order Differential EquationsXTRA-
OCR A-Level (UK - Pre-2017)FP32nd Order Differential EquationsXTRA-
OCR A2 Further Maths 2017Pure CoreExtraDifferential Equations Videos-
OCR MEI A2 Further Maths 2017Core Pure BExtraDifferential Equations Videos-
OCR-MEI A-Level (UK - Pre-2017)DE2nd Order Differential EquationsXTRA-
Scottish Advanced HighersM32nd Order Differential EquationsXTRA-
Scottish (Highers + Advanced)AM32nd Order Differential EquationsXTRA-
Universal (all site questions)S2nd Order Differential EquationsXTRA-