Mathematics category

Differential Equations calculators

Models whose unknown quantities change with time or position.

116 calculators in this category. Page 1 of 3.

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growth and decayoscillationsnumerical solutions

Differential Equations

Exponential growth ODE

Solve y′=ky from an initial value and evaluate the solution at time t.

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Half-life decay

Model exponential decay from an initial amount, half-life and elapsed time.

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Logistic growth ODE

Evaluate population growth with a carrying capacity using the logistic differential equation.

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Newton cooling

Estimate an object's temperature as it approaches a constant ambient temperature.

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First-order linear ODE

Solve y′+py=q with constant coefficients and an initial value.

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Euler method step

Approximate one step for y′=ay+b using the slope at the current point.

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Harmonic oscillator

Evaluate displacement and velocity for x″+ω²x=0 with amplitude and phase.

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Damped oscillator

Evaluate an underdamped oscillation x(t)=Ae⁻ᵝᵗcos(ωt+φ) and its decaying envelope.

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Exponential ODE Advance

Calculate advanced state from initial state and integrated rate kt.

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Exponential ODE Advance: solve initial state

Rearrange the exponential ode advance relationship and solve for initial state.

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Exponential ODE Advance: solve integrated rate kt

Rearrange the exponential ode advance relationship and solve for integrated rate kt.

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Half-Life Period Count

Calculate remaining quantity from initial quantity and elapsed half-lives.

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Half-Life Period Count: solve initial quantity

Rearrange the half-life period count relationship and solve for initial quantity.

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Half-Life Period Count: solve elapsed half-lives

Rearrange the half-life period count relationship and solve for elapsed half-lives.

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Euler State Increment

Calculate euler increment from derivative at current state and time step.

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Euler State Increment: solve derivative at current state

Rearrange the euler state increment relationship and solve for derivative at current state.

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Euler State Increment: solve time step

Rearrange the euler state increment relationship and solve for time step.

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Oscillator Angular-Frequency Squared

Calculate angular frequency squared from spring stiffness and oscillating mass.

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Oscillator Angular-Frequency Squared: solve spring stiffness

Rearrange the oscillator angular-frequency squared relationship and solve for spring stiffness.

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Oscillator Angular-Frequency Squared: solve oscillating mass

Rearrange the oscillator angular-frequency squared relationship and solve for oscillating mass.

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Integrating-Factor Exponential

Calculate integrating factor from initial multiplier and integrated coefficient.

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Integrating-Factor Exponential: solve initial multiplier

Rearrange the integrating-factor exponential relationship and solve for initial multiplier.

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Integrating-Factor Exponential: solve integrated coefficient

Rearrange the integrating-factor exponential relationship and solve for integrated coefficient.

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Relaxation Decay Factor

Calculate remaining displacement from initial displacement from equilibrium and dimensionless elapsed relaxation.

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Relaxation Decay Factor: solve initial displacement from equilibrium

Rearrange the relaxation decay factor relationship and solve for initial displacement from equilibrium.

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Relaxation Decay Factor: solve dimensionless elapsed relaxation

Rearrange the relaxation decay factor relationship and solve for dimensionless elapsed relaxation.

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Time Constant from Reciprocal Rate

Calculate time constant from positive rate constant and unit scale.

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Time Constant from Reciprocal Rate: solve positive rate constant

Rearrange the time constant from reciprocal rate relationship and solve for positive rate constant.

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Time Constant from Reciprocal Rate: solve unit scale

Rearrange the time constant from reciprocal rate relationship and solve for unit scale.

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Exponential Mode Amplification

Calculate amplified mode from initial mode amplitude and integrated growth exponent.

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Exponential Mode Amplification: solve initial mode amplitude

Rearrange the exponential mode amplification relationship and solve for initial mode amplitude.

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Exponential Mode Amplification: solve integrated growth exponent

Rearrange the exponential mode amplification relationship and solve for integrated growth exponent.

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Damping Logarithmic Decrement

Calculate logarithmic decrement from positive earlier peak amplitude and positive later peak amplitude.

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Damping Logarithmic Decrement: solve positive earlier peak amplitude

Rearrange the damping logarithmic decrement relationship and solve for positive earlier peak amplitude.

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Damping Logarithmic Decrement: solve positive later peak amplitude

Rearrange the damping logarithmic decrement relationship and solve for positive later peak amplitude.

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Reaction Rate–Timestep Number

Calculate dimensionless reaction step from reaction rate magnitude and time-step width.

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Reaction Rate–Timestep Number: solve reaction rate magnitude

Rearrange the reaction rate–timestep number relationship and solve for reaction rate magnitude.

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Reaction Rate–Timestep Number: solve time-step width

Rearrange the reaction rate–timestep number relationship and solve for time-step width.

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Wave Grid Points per Wavelength

Calculate grid points per wavelength from represented wavelength and spatial grid spacing.

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Wave Grid Points per Wavelength: solve represented wavelength

Rearrange the wave grid points per wavelength relationship and solve for represented wavelength.

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Wave Grid Points per Wavelength: solve spatial grid spacing

Rearrange the wave grid points per wavelength relationship and solve for spatial grid spacing.

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One-Dimensional Diffusion RMS Length

Calculate root-mean-square diffusion length from twice the positive diffusivity and positive elapsed time.

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One-Dimensional Diffusion RMS Length: solve twice the positive diffusivity

Rearrange the one-dimensional diffusion rms length relationship and solve for twice the positive diffusivity.

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One-Dimensional Diffusion RMS Length: solve positive elapsed time

Rearrange the one-dimensional diffusion rms length relationship and solve for positive elapsed time.

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Linear Forced Steady-State Response

Calculate steady-state response from constant forcing magnitude and positive restoring rate.

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Linear Forced Steady-State Response: solve constant forcing magnitude

Rearrange the linear forced steady-state response relationship and solve for constant forcing magnitude.

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Linear Forced Steady-State Response: solve positive restoring rate

Rearrange the linear forced steady-state response relationship and solve for positive restoring rate.

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ODE Step Amplification Factor

Calculate step amplification factor from new perturbation norm and previous perturbation norm.

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