What’s on the Exact Equations poster
The rule, 3 worked examples, and the mistake everyone makes.
- M dx + N dy = 0 is exact when the partial of M in y equals the partial of N in x, and…
- ∂M/∂y = ∂N/∂x ⇒ F(x, y) = C
- 2xy dx + x² dy = Exact, F = x²y
- y dx − x dy = Not exact
- Test fails = Seek μ(x) or μ(y)
- Common mistake: Testing whether ∂M/∂x equals ∂N/∂y → Testing whether ∂M/∂y equals ∂N/∂x
Find F by integrating M with respect to x, then differentiating in y and matching N. The constant of integration is a function of y.
Questions about the Exact Equations poster
- What’s on the Exact Equations poster?
- The rule, 3 worked examples, and the mistake everyone makes. M dx + N dy = 0 is exact when the partial of M in y equals the partial of N in x, and…; ∂M/∂y = ∂N/∂x ⇒ F(x, y) = C; 2xy dx + x² dy = Exact, F = x²y; y dx − x dy = Not exact; Test fails = Seek μ(x) or μ(y); Common mistake: Testing whether ∂M/∂x equals ∂N/∂y → Testing whether ∂M/∂y equals ∂N/∂x. Find F by integrating M with respect to x, then differentiating in y and matching N. The constant of integration is a function of y.
- Who is the Exact Equations poster for?
- Exact Equations 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 Exact Equations poster?
- For a first-order equation written as M dx + N dy = 0. A wall chart earns its place by being glanceable from where the work is happening, so Exact Equations belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
- What other posters go with Exact Equations?
- Existence & Uniqueness, Separable Equations and Fourier Series sit alongside Exact Equations in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Existence & UniquenessSeparable EquationsFourier Series
- Is the Exact Equations poster free to download and print?
- Yes. Exact Equations 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 Exact Equations poster print at?
- Exact Equations 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 Exact Equations loses nothing.Printing guide
Related posters
Charts that sit alongside Exact Equations on the same wall.
Browse every Mathematics poster, or start from the full catalogue.