🌊 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
🌊 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
🪂 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
🪂 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
🐌 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
🐌 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
⚖️ 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
⚖️ 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
📈 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
📈 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
🔋 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
🔋 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
#Mathematics #FP2 #ALevel #Further
#Mathematics #FP2 #ALevel #Further
🐇 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
🐇 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
#QuantumAlgorithms #DifferentialEquations #Research
#QuantumAlgorithms #DifferentialEquations #Research
🔊 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
🔊 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
📉 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
📉 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
🔢 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
🔢 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
🧬 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
🧬 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
Explore this year’s differential equations modeling challenges: www.contest.comap.com/scudem/2026_...
#SCUDEM #MathModeling #DifferentialEquations
Explore this year’s differential equations modeling challenges: www.contest.comap.com/scudem/2026_...
#SCUDEM #MathModeling #DifferentialEquations
⚖️ 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
⚖️ 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
💓 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
💓 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
🌊 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
🌊 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
☢️ 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
☢️ 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
dy/dx = 0.5y, y(0) = 1
One simple ordinary differential equation. One dramatic curve. Solved with our free ODE solver.
#ODE #DifferentialEquations #STEM
dy/dx = 0.5y, y(0) = 1
One simple ordinary differential equation. One dramatic curve. Solved with our free ODE solver.
#ODE #DifferentialEquations #STEM
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
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
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
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
Bring your team together and register at scudem.org.
#SCUDEM #MathematicalModeling #DifferentialEquations
Bring your team together and register at scudem.org.
#SCUDEM #MathematicalModeling #DifferentialEquations
➡️ hermathsstory.eu/gervy-marie-...
#DifferentialEquations #RoleModels #WomenInMaths #HerMathsStory
➡️ hermathsstory.eu/gervy-marie-...
#DifferentialEquations #RoleModels #WomenInMaths #HerMathsStory
Learn more and register by October 16: scudem.org
#SCUDEM #MathModeling #DifferentialEquations #STEM
Learn more and register by October 16: scudem.org
#SCUDEM #MathModeling #DifferentialEquations #STEM