How do i code linear Ordinary differentiation?

How do i plot linear Ordinary differentiation dy/dx-y =x ........Y= -x -1+ce?

Answer 1

[Suman Sahu]

Hi Mandla,

Your ordinary differential equation can be written as dy/dx = x + y. To plot the differential equation you have to first solve the equation for which you can use any of the ode solvers, eg. ode45 and then use the plot function to plot the generated solution.

Here is an example code for the given ODE.

%step 1: define the function, which is the right hand side of the equation when you write your ode in above format.
f = @(x,y)(x + y); 

The ode45() function has the following syntax:

ode45(f, [Xi Xf], Yi);

where f is the equation in terms of variables x and y.

[Xi Xf] are the lower and upper limits of x for which equation will be integrated.

Yi is the initial value of the variable y.

%step 2: solve the equation, here I've assumed the parameters for this example. 
[x, y] = ode45(f, [0 10], 0); 

%Step 3: plot the solution 
plot(x, y); 

Refer to the following documentation to learn more about different types of ode solvers available:

Ordinary Differential Equations - MATLAB & Simulink

Hope it helps!