Im new at matlab

Hello, im new at matlab and I´d like to solve this ED x2y′′−xy′+y=xln3x, when I put the code i get an error that says "Error in (line 3)

sol = dsolve(eqn)", and no solution is shown in the screen. Also, how do I graphic the family curves of the solutions indicating the parameters I used?

My code is :

syms x y(x)
eqn = x^2*diff(y,x,2) - x*diff(y,x) + y == x*log(3*x);
sol = dsolve(eqn);
disp(sol);

[Voss]

What's the complete error message?

Your code runs without error here:

syms x y(x)
eqn = x^2*diff(y,x,2) - x*diff(y,x) + y == x*log(3*x);
sol = dsolve(eqn);
disp(sol);

[Carlos Julian]

Dont know why I got that error, I was trying the online app and it seems that it was struggling with 3rd line, I moved to the software and got the same answer than yours. Thanxs anyway.

Do you have any idea about the second part of my question? Greetings.

[Torsten]

You have to specify two conditions on y and/or dy in order to fix a solution.

I don't know what you mean by "how do I graphic the family curves of the solutions indicating the parameters I used? " As far as I can see, you don't use parameters in your differential equation.

syms x y(x)
dy = diff(y,x);
d2y = diff(dy,x);
eqn = x^2*d2y - x*dy + y == x*log(3*x);
conds = [y(1)==1,dy(1)==0];
sol = dsolve(eqn,conds);
fplot(sol,[1 5])
grid on

Answer 1

[Arnav]

Hi @Carlos Julian,

I understand that you have solved the given differential equation symbolically and are trying to plot the family of curves represented by the solution.

This can be achieved by substituting different values of C1 and C2 using subs function and plotting them using the plot function. The related code is provided below:

syms x C2 C1 
C1_vals = [1, 2, 3]; % Fixed values for C1 
C2_vals = [-1, 0, 1]; % Values for C2 
x_vals = linspace(0.1, 10, 100); % Range for x 
sol = C2*x - (x*log(x)^2*(log(27) + 2*log(x)))/6 + (x*log(3*x)^2*log(x))/2 + C1*x*log(x); 

for C1_value = C1_vals 
    figure; % Create a new figure for each value of C1 
    hold on; % Hold on to plot multiple lines in the same figure 
    for C2_value = C2_vals 
        y = subs(sol,[C1 C2], [C1_value C2_value]); 
        y_vals = double(subs(y, x, x_vals)); % Evaluate for x 
        plot(x_vals, y_vals, 'DisplayName', sprintf('C2=%.1f', C2_value)); 
    end 
    hold off; % Release hold after plotting 
    xlabel('x'); ylabel('y'); 
    title(sprintf('Curves for C1=%.1f', C1_value)); legend('show'); 
end 

You may refer to the following documentation links for more information about the functions subs and plot:

• subs: https://www.mathworks.com/help/symbolic/sym.subs.html
• plot: https://www.mathworks.com/help/matlab/ref/plot.html