What’s on the Second-Order Linear ODEs poster
A 4-row table: Discriminant · Roots m · General solution.
For ay″ + by′ + cy = 0, try y = e^(mx).
- b² − 4ac > 0 — Real and distinct — A e^(m₁x) + B e^(m₂x)
- b² − 4ac = 0 — Real and repeated — (A + Bx) e^(mx)
- b² − 4ac < 0 — p ± qi — e^(px)(A cos qx + B sin qx)
- b = 0 with ac > 0 — Purely imaginary ±qi — A cos qx + B sin qx
The three cases are overdamped, critically damped and underdamped. Critical damping returns to rest fastest without overshooting.
Questions about the Second-Order Linear ODEs poster
- What’s on the Second-Order Linear ODEs poster?
- A 4-row table: Discriminant · Roots m · General solution. For ay″ + by′ + cy = 0, try y = e^(mx). b² − 4ac > 0 — Real and distinct — A e^(m₁x) + B e^(m₂x); b² − 4ac = 0 — Real and repeated — (A + Bx) e^(mx); b² − 4ac < 0 — p ± qi — e^(px)(A cos qx + B sin qx); b = 0 with ac > 0 — Purely imaginary ±qi — A cos qx + B sin qx. The three cases are overdamped, critically damped and underdamped. Critical damping returns to rest fastest without overshooting.
- Who is the Second-Order Linear ODEs poster for?
- Second-Order Linear ODEs 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 Second-Order Linear ODEs poster?
- For any constant-coefficient homogeneous equation, and for damped oscillators. A wall chart earns its place by being glanceable from where the work is happening, so Second-Order Linear ODEs belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
- What other posters go with Second-Order Linear ODEs?
- Exact Equations, Existence & Uniqueness and Separable Equations sit alongside Second-Order Linear ODEs in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Exact EquationsExistence & UniquenessSeparable Equations
- Is the Second-Order Linear ODEs poster free to download and print?
- Yes. Second-Order Linear ODEs 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 Second-Order Linear ODEs poster print at?
- Second-Order Linear ODEs 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 Second-Order Linear ODEs loses nothing.Printing guide
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