What’s on the Undetermined Coefficients poster
A 6-row table: Forcing term f(x) · Trial particular integral.
For ay″ + by′ + cy = f(x), guess the shape of f.
- A constant k — A
- Polynomial of degree n — A full polynomial of degree n
- e^(kx) — A e^(kx)
- sin ωx or cos ωx — A cos ωx + B sin ωx
- e^(kx) sin ωx — e^(kx)(A cos ωx + B sin ωx)
- Trial duplicates a CF term — Multiply the whole trial by x
If the trial already solves the homogeneous equation, multiply it by x — and by x² again if it still does. Then match coefficients.
Questions about the Undetermined Coefficients poster
- What’s on the Undetermined Coefficients poster?
- A 6-row table: Forcing term f(x) · Trial particular integral. For ay″ + by′ + cy = f(x), guess the shape of f. A constant k — A; Polynomial of degree n — A full polynomial of degree n; e^(kx) — A e^(kx); sin ωx or cos ωx — A cos ωx + B sin ωx; e^(kx) sin ωx — e^(kx)(A cos ωx + B sin ωx); Trial duplicates a CF term — Multiply the whole trial by x. If the trial already solves the homogeneous equation, multiply it by x — and by x² again if it still does. Then match coefficients.
- Who is the Undetermined Coefficients poster for?
- Undetermined Coefficients belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning differential equations can pin it up — a beginner, a student mid-course, or someone revising years later.
- When should you use the Undetermined Coefficients poster?
- For a non-homogeneous equation whose right side is a familiar shape. A wall chart earns its place by being glanceable from where the work is happening, so Undetermined Coefficients belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
- What other posters go with Undetermined Coefficients?
- Variation of Parameters, Exact Equations and Existence & Uniqueness sit alongside Undetermined Coefficients in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Variation of ParametersExact EquationsExistence & Uniqueness
- Is the Undetermined Coefficients poster free to download and print?
- Yes. Undetermined Coefficients downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
- What size does the Undetermined Coefficients poster print at?
- Undetermined Coefficients is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Undetermined Coefficients loses nothing.Printing guide
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