#DifferentialEquations
𝐁𝐞𝐬𝐬𝐞𝐥’𝐬 𝐄𝐪𝐮𝐚𝐭𝐢𝐨𝐧

🌊 This ordinary differential equation appears everywhere: drum vibrations, heat conduction in cylinders, electromagnetic waves.

y’’ = (-y’ - y)/x

Solved with our free ODE solver.

#ODE #DifferentialEquations #MathPhysics
November 4, 2026 at 2:19 AM
𝐅𝐫𝐞𝐞 𝐅𝐚𝐥𝐥 𝐰𝐢𝐭𝐡 𝐀𝐢𝐫 𝐑𝐞𝐬𝐢𝐬𝐭𝐚𝐧𝐜𝐞

🪂 Dropping from 1000m with air drag. This second-order ordinary differential equation shows how terminal velocity limits the fall.

y’’ = -9.8 + 0.1(y’)²

Solved with our free ODE solver.

#odesolver #DifferentialEquations #physics
October 31, 2026 at 1:12 AM
𝐎𝐯𝐞𝐫𝐝𝐚𝐦𝐩𝐞𝐝 𝐒𝐲𝐬𝐭𝐞𝐦

🐌 Too much damping, too slow to recover. This ordinary differential equation shows a system crawling back to zero without ever oscillating.

y’’ = -5y’ - 4y

Plotted with our free ODE solver.

#ODE #DifferentialEquations #MechanicalEngineering
November 2, 2026 at 11:22 PM
𝐂𝐫𝐢𝐭𝐢𝐜𝐚𝐥𝐥𝐲 𝐃𝐚𝐦𝐩𝐞𝐝 𝐒𝐲𝐬𝐭𝐞𝐦

⚖️ The fastest return to equilibrium without oscillation. This ordinary differential equation is how engineers design car suspensions and door closers.

y’’ = -2y’ - y

Solved with our free ODE solver.

#ODE #DifferentialEquations #Engineering
November 1, 2026 at 4:42 PM
𝐇𝐲𝐩𝐞𝐫𝐛𝐨𝐥𝐢𝐜 𝐒𝐢𝐧𝐞 𝐆𝐫𝐨𝐰𝐭𝐡

📈 Explosive growth driven by a hyperbolic sine. This ordinary differential equation accelerates faster than exponential.

dy/dx = sinh(y/10)

Plotted with our free ODE solver.

#odesolver #DifferentialEquations #mathematics
October 31, 2026 at 9:57 PM
𝐑𝐂 𝐂𝐢𝐫𝐜𝐮𝐢𝐭 𝐂𝐡𝐚𝐫𝐠𝐢𝐧𝐠

🔋 A capacitor charging through a resistor. This ordinary differential equation shows voltage rising from 0 toward 5V. The same math behind every phone charger.

dy/dx = (5 - y)/2

Plotted with our free ODE solver.

#odesolver #DifferentialEquations #electronics
October 30, 2026 at 8:47 PM
I really shouldn't try and solve second-order non-homogeneous #DifferentialEquations when I'm tired.

#Mathematics #FP2 #ALevel #Further
October 27, 2026 at 4:21 AM
𝐏𝐫𝐞𝐲 𝐏𝐨𝐩𝐮𝐥𝐚𝐭𝐢𝐨𝐧 (𝐋𝐨𝐭𝐤𝐚-𝐕𝐨𝐥𝐭𝐞𝐫𝐫𝐚)

🐇 How a prey population grows with limited resources. This ordinary differential equation combines exponential growth with a carrying capacity.

dy/dx = 0.4y - 0.01y²

Solved with our free ODE solver.

#ODE #DifferentialEquations #Ecology
October 23, 2026 at 1:37 AM
Develops quantum algorithm for solving high-dimensional nonlinear stochastic differential equations using Carleman linearization, achieving polylogarithmic query complexity in dimension and exponential error decay with truncation order.

#QuantumAlgorithms #DifferentialEquations #Research
Quantum Algorithm for High-Dimensional Nonlinear Stochastic Differential Equations via Carleman Linearization
arxiv.org
October 21, 2026 at 3:58 AM
𝐃𝐫𝐢𝐯𝐞𝐧 𝐎𝐬𝐜𝐢𝐥𝐥𝐚𝐭𝐨𝐫

🔊 Push a spring with a periodic force and watch what happens. This ordinary differential equation shows transient chaos settling into steady oscillation.

y’’ = -0.3y’ - y + cos(x)

Solved with our free ODE solver.

#ODE #DifferentialEquations #PhysicsQuiz
October 21, 2026 at 1:19 AM
𝐃𝐚𝐦𝐩𝐞𝐝 𝐎𝐬𝐜𝐢𝐥𝐥𝐚𝐭𝐨𝐫

📉 What happens when friction slows a vibrating system? This ordinary differential equation shows oscillations dying out over time.

y’’ = -0.5y’ - 4y

Plotted with our free ODE solver.

#ODE #DifferentialEquations #engineering
October 19, 2026 at 10:22 PM
𝐑𝐢𝐜𝐜𝐚𝐭𝐢 𝐄𝐪𝐮𝐚𝐭𝐢𝐨𝐧

🔢 The Riccati ordinary differential equation: dy/dx = y² - x

A nonlinear ODE with no general closed-form solution. Numerical methods like RK4 are the only way forward.

Solved with our free ODE solver.

#ODE #DifferentialEquations #mathematics
October 18, 2026 at 3:42 PM
𝐆𝐨𝐦𝐩𝐞𝐫𝐭𝐳 𝐆𝐫𝐨𝐰𝐭𝐡 𝐌𝐨𝐝𝐞𝐥

🧬 How tumors grow: fast at first, then slowing as they get larger. The Gompertz ordinary differential equation models this self-limiting growth.

dy/dx = -0.3y·ln(y/100)

Plotted with our free ODE solver.

#ODE #DifferentialEquations #BIOMATH
October 17, 2026 at 9:57 PM
The SCUDEM XI 2026 problems are here! What will your team model?

Explore this year’s differential equations modeling challenges: www.contest.comap.com/scudem/2026_...

#SCUDEM #MathModeling #DifferentialEquations
October 16, 2026 at 7:18 PM
𝐁𝐞𝐫𝐧𝐨𝐮𝐥𝐥𝐢 𝐄𝐪𝐮𝐚𝐭𝐢𝐨𝐧

⚖️ dy/dx = y - y²

A classic ordinary differential equation where linear growth battles quadratic decay until equilibrium wins.

Solved with our free ODE solver.

#ODE #DifferentialEquations #mathematics
October 16, 2026 at 1:37 AM
𝐕𝐚𝐧 𝐝𝐞𝐫 𝐏𝐨𝐥 𝐎𝐬𝐜𝐢𝐥𝐥𝐚𝐭𝐨𝐫

💓 y’’ = 3(1 - y²)y’ - y

This nonlinear ordinary differential equation produces self-sustaining oscillations. Used to model heartbeats and biological rhythms.

Plotted with our free ODE solver.

#ODE #DifferentialEquations #NonlinearDynamics
October 15, 2026 at 1:43 AM
𝐇𝐚𝐫𝐦𝐨𝐧𝐢𝐜 𝐎𝐬𝐜𝐢𝐥𝐥𝐚𝐭𝐨𝐫

🌊 y’’ = -y

The most fundamental ordinary differential equation in physics. Pure sinusoidal motion, no damping, no driving force.

Solved with our free ODE solver.

#ODE #DifferentialEquations #STEM
October 14, 2026 at 1:19 AM
𝐑𝐚𝐝𝐢𝐨𝐚𝐜𝐭𝐢𝐯𝐞 𝐃𝐞𝐜𝐚𝐲

☢️ Radioactive decay as an ordinary differential equation: dy/dx = -0.3y

The same ODE behind cooling, drug metabolism, and capacitor discharge. Solved with our free ODE solver.

#ODE #DifferentialEquations #Physics
October 11, 2026 at 8:31 PM
📈 What unchecked growth really looks like.

dy/dx = 0.5y, y(0) = 1

One simple ordinary differential equation. One dramatic curve. Solved with our free ODE solver.

#ODE #DifferentialEquations #STEM
October 11, 2026 at 1:27 AM
𝐋𝐨𝐠𝐢𝐬𝐭𝐢𝐜 𝐄𝐪𝐮𝐚𝐭𝐢𝐨𝐧

What happens when growth hits a ceiling? 📊

This ordinary differential equation shows how populations level off at their carrying capacity.

dy/dx = 0.5y(1 - y/10)

Plotted with our free ODE solver.

#ODE #DifferentialEquations #ScienceEducation
October 11, 2026 at 10:44 AM
There’s still time to get a team involved in SCUDEM XI!

We put together six reasons to participate: www.comap.org/blog/item/re...

Registration closes October 16 at 2:00 p.m. ET. Visit scudem.org to register.

#SCUDEM #MathModeling #DifferentialEquations #MathEducation
October 9, 2026 at 1:34 PM
SCUDEM starts next week! Teams of up to 3 students will choose a challenge, build a model, and share their findings in a 10-minute video presentation.

Bring your team together and register at scudem.org.

#SCUDEM #MathematicalModeling #DifferentialEquations
October 7, 2026 at 7:19 PM
“People often assume it means being a human calculator. But #mathematics is vast, a language, a science, and an art. More people should know this.” - Gervy Marie Angeles

➡️ hermathsstory.eu/gervy-marie-...

#DifferentialEquations #RoleModels #WomenInMaths #HerMathsStory
September 30, 2026 at 10:02 AM
SCUDEM challenges you to gather a team of up to three students, choose a problem in physics and engineering, chemistry and life sciences, or social sciences, and build a model to explore it.

Learn more and register by October 16: scudem.org

#SCUDEM #MathModeling #DifferentialEquations #STEM
September 30, 2026 at 12:44 PM