Second Order ODE solve

Solve the following equation. Your answer must be real-valued functions and must be simplified.

y'' + 4y = f(x), f(x) = sin(2x) when pi/4 < x < 3*pi/4 and f(x) = 0 when otherwise

Given y(pi/4) = 3, y(pi/2) = 0.

Answer 1

[Ashutosh Singh Baghel]

Hi Patiphol,

I believe you wish to plot this second order ode dependent on x. Please find a reference example

fx = linspace(0, 10, 50);
f = sin(2*fx);
xspan = [pi*0.25 pi*0.5];
y_0 = [3 0];
[x,y] = ode45(@(x, y) myode1(x, y, fx, f), xspan, y_0);
plot(x, y(:,1), '-r ', x, y(:,2), '--g');
legend('y(1)', 'y(2)');
xlabel('x');
ylabel('y Solution');

function dydx = myode1(x, y, fx, f)
f = interp1(fx, f, x);
dydx = [y(2); f - 4*y(1)]; 
end

Please refer to the following MATLAB Documentation page on the 'ode45' function and relevant information on the 'Differential Equation'.