For the classes of Atul Roy
script
% ode45 is a built-in MATLAB function to find numerical solutions to differential equations.
% It gives more accurate results than Euler's method by adjusting step sizes automatically.
% Define the ODE as a function: dy/dx = sin(xy/2) + (2x/sqrt(y^2+1)
f = @(x, y) sin(x*y/2) + 2*x/sqrt(y^2+1);
% Solve the ODE from x = 0 to x = 2 with initial condition y(0) = 1
[x_vals, y_vals] = ode45(f, [0 2], 1);
% Plot the solution
plot(x_vals, y_vals), xlabel('x'), ylabel('y(x)')
title('Solution of dy/dx = sin(xy/2) + (2x/sqrt(y^2+1)')
% Approximate y at x = 1, with interp1 to interpolate
y_at_1 = interp1(x_vals, y_vals, 1);
fprintf('Approximate value of y at x = 1: %.6f\n', y_at_1)
%\n is newline character — it tells MATLAB to go to the next line after printing.
%So '%.6f\n' means: print the number with 6 decimal places, then move to a new line.
