Question

Solve the cauchy problem (x^2)*y''-9*x*y'+21*y=0, y'(1)=5 on the interval (1,3). Plot the graphs of y(x) and y'(x)

Please Provide only MATLAB Code.

Answer 1

%%Matlab code for solving ode
clear all
close all
%Answering question
%Initial conditions for ode
    u0=[0;5];
  
%Solution for equation 1. using ode45
        %minimum and maximum time span
        xspan=[1 3];
        %Solution of ODEs using ode45 matlab function
        [x1,sol1]= ode45(@(x,y) odefcn1(x,y), xspan, u0);

        %Plotting the solution
        figure(1)
        plot(x1,sol1(:,1))
        title('x vs. y(x) plot for ode45')
        xlabel('x')
        ylabel('y(x)')
      
        figure(2)
        plot(x1,sol1(:,2))
        title('x vs. dy(x)/dx plot for ode45')
        xlabel('x')
        ylabel('dy(x)/dx')
     

%Function for evaluating the ODE
function du1dt = odefcn1(x,y)
    eq1=y(2);
    eq2=(9./x).*y(2)-(21./x.^2).*y(1);
  
    %Evaluate the ODE for our present problem
    du1dt = [eq1;eq2];
end

%%%%%%%%%%%%%%%% End of Code %%%%%%%%%%%%%%%%