Solve Differential Equations with ODEINT Function of SciPy module in Python

In science and engineering, many problems involve quantities that change over time like speed of a moving object or temperature of a cooling cup. These changes are often described using differential equations.

SciPy provides a function called odeint (from the scipy.integrate module) that helps solve these equations numerically. By giving it a function that describes how your system changes and some starting values, odeint calculates how the system behaves over time.

Syntax

scipy.integrate.odeint (func, y₀, t, args=())

Parameter:

• func: function that returns the derivative (dy/dt).
• y₀: initial conditions.
• t: time points to solve the ODE at.
• args (optional): extra values passed to func.

Solving Differential Equations

Let's solve an ordinary differential equation (ODE) using the odeint() function.

Example 1

Output

Explanation:

• Defines and solves the ODE dy/dt = -y * t + 13 using odeint with initial value y = 1.
• The graph shows how y changes over time.
• y increases first then slows as -y * t term grows.

Example 2

Output

Explanation:

• Defines and solves ODE dy/dt = 13*eᵗ + y using odeint starting from y = 1.
• The graph shows y grows rapidly, driven by both exponential and linear terms.
• The exponential term accelerates the growth of y as time increases.

Example 3

Output

Explanation:

• Defines and solves ODE dy/dt = (1−y)/(1.95−y) − y/(0.05+y) using odeint with initial values y = 0, 1 and 2.
• The graph shows how y evolves over time for each initial value.
• The equation models a system with competing growth and decay rates, influenced by the values of y.

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