Existence & UniquenessWhat guarantees a solution, what guarantees only one, and how local both are.MathematicsIf f is continuous near the initial point a solutionexists; if the partial of f in y is also continuous, it isunique.f continuous ⇒ exists · ∂f/∂y too ⇒ uniquey′ = y, y(0) = 1Unique: y = e^xBoth conditions hold.y′ = √y, y(0) = 0Not unique∂f/∂y blows up.y′ = 1 + y², y(0) = 0Unique but escapesOnly local existence.THE COMMON MISTAKE✗ Reading the theorem as a global promise✓ It is local: some interval around x₀y′ = 1 + y² with y(0) = 0 gives y = tan x, which exists only up to π/2 even thoughf is perfectly smooth everywhere.Lipschitz continuity in y is the sharp condition. Continuity of the partialderivative is the version that is easy to check.Existence & Uniquenesslearnposters.com
Existence & Uniqueness — printable math wall chart from LearnPosters. Free vector PDF, US Letter and A4.

What’s on the Existence & Uniqueness poster

The rule, 3 worked examples, and the mistake everyone makes.

Lipschitz continuity in y is the sharp condition. Continuity of the partial derivative is the version that is easy to check.

Questions about the Existence & Uniqueness poster

What’s on the Existence & Uniqueness poster?
The rule, 3 worked examples, and the mistake everyone makes. If f is continuous near the initial point a solution exists; if the partial of f in y…; f continuous ⇒ exists · ∂f/∂y too ⇒ unique; y′ = y, y(0) = 1 = Unique: y = e^x; y′ = √y, y(0) = 0 = Not unique; y′ = 1 + y², y(0) = 0 = Unique but escapes; Common mistake: Reading the theorem as a global promise → It is local: some interval…. Lipschitz continuity in y is the sharp condition. Continuity of the partial derivative is the version that is easy to check.
Who is the Existence & Uniqueness poster for?
Existence & Uniqueness 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 Existence & Uniqueness poster?
Before assuming an initial-value problem has exactly one solution. A wall chart earns its place by being glanceable from where the work is happening, so Existence & Uniqueness belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
What other posters go with Existence & Uniqueness?
Solving ODEs by Laplace, Exact Equations and Separable Equations sit alongside Existence & Uniqueness in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Solving ODEs by LaplaceExact EquationsSeparable Equations
Is the Existence & Uniqueness poster free to download and print?
Yes. Existence & Uniqueness 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 Existence & Uniqueness poster print at?
Existence & Uniqueness 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 Existence & Uniqueness loses nothing.Printing guide

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