MATLAB: How to solve the differential equation numerically which is of the form : (z”/[1+(z’)^2]^(3/2))+(0.1928529/x)=2+(50.99203)*z ? I need to get the x and z values.

differential equationsnumerical integrationodeode45

Initial conditions are x=0 and z=0

Start with this:

(z"/[1+(z')^2]^(3/2))+(0.1928529/x)=2+(50.99203)*z

Solve for the highest order derivative z"

z" = [1+(z')^2]^(3/2) * (2 + (50.99203)*z - (0.1928529/x))

And then follow the examples in the ode45 doc for solving a 2nd order ODE. E.g., the derivative function

dzdx = @(x,z) [z(2);  ((1+z(2)^2)^(3/2)) * (2 + (50.99203)*z(1) - (0.1928529/x))

The initial vector assuming the initial value z' = 0 (you didn't specify)

z0 = [0;0];

See the following link:

Download the file and open the m file within. Find the code for the method.

I would first define ‘f(z)’ as:

f = @(z) 34.*(z>1) - 34.*(z<-1);

then create a separate anonymous function for the system of differential equations, calling ‘f(z)’:

dx/dt = y - 2*x + f(z)

and the other two equations, using the appropriate vector elements for ‘x’, ‘y’, and ‘z’.

I already coded and ran this, and it is straightforward. Forum convention discourages our posting complete solutions, to homework assignments.

Give it a go. If you have problems, we will help.