University Differential Equations First-Order Solution Methods — Unit Notes
Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 6 definitions and 7 theorems, 7 worked examples, 2 diagrams, in 16 printable pages. This page lists what the notes cover. The notes themselves come with the University Differential Equations bundle.
Unit notes — in the bundle
Not sold separately. The practice worksheet for this unit is free, with no email and no account.
First-Order Solution Methods — what the notes cover
8 sections, in the order the unit is taught. Each entry below is the title of a definition or a theorem the notes state in full.
What you need
Also in this section: 1 note on method and common errors.
Separable equations, implicit and lost solutions
- Definition — Separable equation
- Theorem — Separating the variables
- Definition — Interval of validity
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Linear equations and the integrating factor
- Definition — Linear first-order equation
- Theorem — Solution by an integrating factor
Also in this section: 1 worked example, 1 note on method and common errors.
Exact equations
- Definition — Exact equation
- Theorem — Test for exactness, and recovery of
Also in this section: 1 worked example, 1 note on method and common errors.
Integrating factors for equations that are not exact
- Theorem — An integrating factor in one variable
Also in this section: 1 worked example, 1 note on method and common errors.
Homogeneous equations solved by substitution
- Definition — Homogeneous first-order equation
- Theorem — The substitution
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
Bernoulli equations
- Definition — Bernoulli equation
- Theorem — The substitution
Also in this section: 1 worked example, 1 note on method and common errors.
Choosing a method for a first-order equation
- Theorem — Equations in the combination
Also in this section: 1 worked example, 1 note on method and common errors.
Where the notes are
The notes are one of the documents in the University Differential Equations Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The First-Order Solution Methods practice worksheet is free and stays free.
Every University Differential Equations topic — the complete Solutions Bundle
One download, one payment, the whole program. For all 9 University Differential Equations units: the worksheet, the reference notes, the challenge set, the unit test and every answer key — these notes included.
- Worked solutions, not answer lists — every step written out
- Covers the whole year's program at this level
- Less than the price of one hour of tutoring — for the entire year's solutions
Practise it, then test yourself
Notes on their own do not make anything stick. This unit has a free, printable practice worksheet, and an end-of-unit test that comes with the bundle.
First-Order Solution Methods practice worksheet About the First-Order Solution Methods unit test