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This lecture from MIT is about 45 minutes long delivered by Professor David Jerison and covers the solution of differential equations by separating the variables.

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.

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solution

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This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AP Calculus AB (USA)41st Order Differential EquationsXTRA-
AP Calculus BC (USA)41st Order Differential EquationsXTRA-
AQA A-Level (UK - Pre-2017)FP31st Order Differential EquationsXTRA-
AQA A2 Further Maths 2017Pure MathsExtraDifferential Equations Videos-
AQA AS/A2 Further Maths 2017Pure MathsExtraDifferential Equations Videos-
CCEA A-Level (NI)FP21st Order Differential EquationsXTRA-
Edexcel A-Level (UK - Pre-2017)FP21st Order Differential EquationsXTRA-
Edexcel A2 Further Maths 2017Core Pure MathsExtra(1st) Differential Equations - Extra-
Edexcel AS/A2 Further Maths 2017Core Pure MathsExtra(1st) Differential Equations - Extra-
I.B. Higher Level91st Order Differential EquationsXTRA-
Methods (UK)M111st Order Differential EquationsXTRA-
OCR A-Level (UK - Pre-2017)C41st 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)DE1st Order Differential EquationsXTRA-
Universal (all site questions)F1st Order Differential EquationsXTRA-
WJEC A-Level (Wales)C41st Order Differential EquationsXTRA-