How can I solve & this 2nd order differential equation?

% x = x''
% y = x'
% z = x

% Conditions
f = 50:1:200; % Frequency span (Hz)

for f = 50:1:200
    Equation = 50x - 100y - 25z == -1(f * 2 * pi);
    plot(f, Equation)
    hold on
end

Answer 1

[Ameer Hamza]

This shows how to solve this ODE for all values of 'f', and plot the solution as a surf plot

f = 50:1:200;
t = linspace(0, 10, 1000); % solve the equation for t in [0, 10]
ic = [0; 0]; % initial condition
Y = zeros(numel(f), numel(t));

for i = 1:numel(f)
    [~, y] = ode45(@(t, x) odeFun(t, x, f(i)), t, ic);
    Y(i, :) = y(:, 1);
end

surf(t, f, Y);
shading interp
xlabel('t');
ylabel('f');
zlabel('x');

function dxdt = odeFun(t, x, f)
    dxdt = zeros(2, 1);
    dxdt(1) = x(2);
    dxdt(2) = 1/50*(100*x(2) + 25*x(1) - 1*2*pi*f);
end

Also see this example: https://www.mathworks.com/help/matlab/ref/ode45.html#bu3uj8b. It shows how to convert the 2nd-order ODE into a system of 2 first-order ODEs.