How to Use differential equation in a Sentence

differential equation

noun
  • These are differential equations that describe the flow of liquids.
    — Manon Bischoff, Scientific American, 23 Mar. 2023
  • On the left are the differential equations that model the flight of the lunar lander in their textbook form.
    — Stephen Cass, IEEE Spectrum, 28 Dec. 2023
  • Some of the models include up to 100 differential equations just for one cell.
    — Steven Strogatz, Quanta Magazine, 12 July 2023
  • For such differential equations, there is often no exact solution.
    — Manon Bischoff, Scientific American, 24 July 2023
  • Just how can a box of gears, cams, racks, and pins handle ballistics calculations based on differential equations with dozens of variables in real time?
    — Sean Gallagher, Ars Technica, 24 May 2020
  • Every single neuron has to be defined by a number of different variables, and each variable requires a set of differential equations to run.
    — William Herkewitz, Popular Mechanics, 11 July 2014
  • One of Hilbert’s problems, about families of curves defined by differential equations, was considered solved.
    — Quanta Magazine, 22 May 2024
  • This makes for a complicated set of relationships that can be studied using differential equations.
    — Eugenia Cheng, WSJ, 9 Nov. 2018
  • Long’s idea was to build a computer simulation that would model each of the hundred and fifty-odd steps in photosynthesis as a differential equation.
    — Elizabeth Kolbert, The New Yorker, 6 Dec. 2021
  • But there is no universally applicable method for solving these differential equations.
    — Manon Bischoff, Scientific American, 12 May 2026
  • In principle, the onboard computer solved differential equations, which depend not only on variables such as x and y but also on their derivatives.
    — Manon Bischoff, Scientific American, 12 May 2026
  • The impetus this time was the self-duality equation, a nonlinear differential equation that arises in quantum field theory.
    — Quanta Magazine, 4 Mar. 2021
  • This gives us a differential equation—a mathematical relationship between the rate of change of one quantity and some other quantities.
    — Eugenia Cheng, WSJ, 3 June 2021
  • One of his proudest accomplishments is taking differential equations with linear algebra at George Fox during his sophomore year.
    — oregonlive, 21 June 2023
  • This approach describes the WPT circuit using differential equations that capture how voltages and currents evolve within the system.
    — Atharva Gosavi, Interesting Engineering, 6 Aug. 2025
  • Solving the differential equations shows this dependency and leads to some counterintuitive solutions.
    — Eugenia Cheng, WSJ, 9 Nov. 2018
  • The students then learned to map out the likely impact of teeth scrubbing on plaque growth, before pivoting to other possible applications of advanced concepts like vector spaces and differential equations.
    — Daniel Mollenkamp, USA TODAY, 6 Sep. 2023
  • Regardless of whether one studies cosmology, particle physics, medicine or chemical processes, one is always dealing with variable systems and thus with differential equations.
    — Manon Bischoff, Scientific American, 12 May 2026
  • She was hired as a mathematician, joining a cadre of workers who used linear algebra, calculus, and other methods to manually solve complex problems such as differential equations.
    — IEEE Spectrum, 30 July 2024
  • Another plaintiff, Nick Venner, seventeen, dons headphones and begins solving differential equations on his laptop.
    — Julia Felsenthal, Vogue, 21 Mar. 2019
  • Our model described the interaction over time of glucose and insulin by means of differential equations representing the best available estimates of human physiology.
    — Boris Kovatchev, IEEE Spectrum, 21 Nov. 2021
  • Physicists have a lot of experience in dealing with dynamical systems modelling, differential equations, and computer/ data scientists can analyse the data that is available.
    — Bhavya Dore, Quartz India, 8 Apr. 2020
  • The Langlands program relates prime number values of polynomial equations to spectra from the differential equations studied in analysis and geometry.
    — Quanta Magazine, 20 Mar. 2018
  • Five of them will be taking college courses in differential equations, abstract algebra and discrete mathematics as 10th-graders at Pasadena High School this fall.
    — Jay Mathews, Washington Post, 6 July 2019
  • One paper posted in July uses them to construct solutions to a system of differential equations used to model everything from predator-prey interactions to waves traveling in high-energy plasmas.
    — Alex Stone, Quanta Magazine, 16 Nov. 2023
  • Soon enough, mathematicians began to discover deep connections between harmonic analysis and other areas of math and physics, from number theory to differential equations to quantum mechanics.
    — Shalma Wegsman, Quanta Magazine, 3 Sep. 2025
  • The field equations of general relativity consist of 10 nonlinear differential equations that must be solved simultaneously — a task so demanding that exact solutions have only been obtained in a handful of special cases.
    — Steve Nadis, Discover Magazine, 20 Apr. 2023
  • For example, mechanical engineers apply calculus to analyze stress distributions in materials, while electrical engineers use differential equations to design control systems.
    — Srishti Gupta, Interesting Engineering, 29 Aug. 2025
  • Steve Furber, a computer scientist emeritus at the University of Manchester, in England, says this builds on the Sandia team’s previous work implementing another method for solving differential equations, the Monte Carlo method, on neuromorphic hardware.
    — IEEE Spectrum, 2 Feb. 2026

Some of these examples are programmatically compiled from various online sources to illustrate current usage of the word 'differential equation.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

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