Matlab ODE45: Solving the Initial Value Problem dv/dt = -y

This guide demonstrates how to use the ode45 function in Matlab to solve the initial value problem dv/dt = -y with the initial condition y(0) = 1 and a time range of 0 to 5.

Here's the Matlab code:

function dydt = myode(t,y)
dydt = -y;
end

[t,y] = ode45(@myode,[0 5],1);

plot(t,y);
xlabel('t');
ylabel('y');
title('Solution of dv/dt = -y, y(0) = 1');

Explanation of the Code:

• Function Definition (myode): The first line defines a function called myode that takes t and y as input arguments and returns dydt, which represents the right-hand side of the differential equation.
• Solving the Differential Equation (ode45): The third line uses the ode45 function to solve the differential equation. The arguments are:
  • @myode: A function handle that points to the myode function, specifying the right-hand side of the equation.
  • [0 5]: An array representing the time range (from 0 to 5) for which the solution is sought.
  • 1: The initial condition, y(0) = 1.
• Plotting the Solution: The fifth line plots the solution obtained from ode45, displaying the relationship between t and y.