Solutions of First-Order and Reducible Higher-Order Ordinary Differential Equations
3 hrs
Course Chapters
1Introduction
A review of the fundamental concepts of differential equations and an introduction to first-order ordinary differential equations.
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2Separable Equations
Identification and solution of first-order ODEs solvable by separation of the dependent and independent variables.
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3Homogeneous Equations
Meaning and solution of homogeneous first-order ODEs.
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4Transformable Non-Homogeneous Equations
Identifying and solving non-homogeneous first-order ODES transformable to homogeneous and / or separable ones.
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5Exact Equations
Meaning and solution of exact first-order ordinary differential equations.
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6Transformable Inexact Equations (1)
Integrating factors and their use in transforming inexact first-order ODEs into exact ones - special cases.
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7Transformable Inexact Equations (2)
Integrating factors and their use in transforming inexact first-order ODEs into exact ones - by inspection method.
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8Transformable Inexact Equations (3)
Integrating factors and their use in transforming inexact first-order ODEs into exact ones - use of groups.
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9Linear Equations
Meaning, identification and solution of linear first-order ODES.
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10Transformable Non-Linear Equations
Identifying and solving non-linear first-order ODEs transformable to linear ones - Bernoulli and Riccati equations.
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11Variable-Solvable Equations
Identifying and solving first-order ODEs solvable for the dependent or independent variable.
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12Reducible Higher-Order ODEs
Identifying and solving higher-order ODEs reducible to first-order ones - when either the dependent or the independent variable is absent.
Chapter lessons
1.Directly-integrable equations13:26
Solving higher-order ODEs that are directly integrable.
2.Dependent variable absent23:03
Solving higher-order ODEs by reduction to lower-order ones when the dependent variable is absent.
3.Independent variable absent23:17
Solving higher-order ODEs by reduction to lower-order ones when the independent variable is absent.
4.Worked examples (1)16:20
Worked examples on solving reducible higher-order ODEs.
5.Worked examples (2)53:20
More worked examples on solving reducible higher-order ODEs.
6.Worked examples (3)16:54
More worked examples on solving reducible higher-order ODEs.