How do I solve the following second order differential equation?

Can you give me the code on how to solve the following equation?

1.4x'' + 4x' + 1700x = - [-8x' + 20(x')^3 + 100x - 2.5x^3]

Thanks!

Answer 1

[Ramanuja Jagannathan]

Please find below the documentation link showing how to represent differential equations in MATLAB and solve them. https://www.mathworks.com/help/symbolic/solve-a-single-differential-equation.html

Hope this helps

[John O'Brian]

Hi I have the following code:

syms y(t)
[V] = odeToVectorField(1.4*diff(y, 2) == 8*diff(y)-20*(diff(y)).^3-100*y+2.5*y.^3-4*diff(y)-1700*y);
M = matlabFunction(V,'vars', {'t','Y'});
sol = ode45(M,[0 20],[0.01 0]);

opts = odeset('OutputFcn',@odephas2);                   % Options Structure
tspan = linspace(0, 1, 100);                            % Times For Evaluation
ic = [0 1];                                             % Initial Conditions
[t, xt] = ode45(EqnFcn, tspan, ic);                 
figure(1)
[t, xt] = ode45(EqnFcn, tspan, ic, opts);
title('Phase Plane Plot')
axis equal
figure(2)
plot(t, xt)
grid on
title('Time Domain Plot')
EqnSubc = regexp(sprintf('%s\n',Eqn_subs), '\n','split');
legend(EqnSubc{1:end-1})

I am trying to plot a phase plane plot for a variety of initial conditions. I think it might require a for loop. Can you adjust the code and show me how to do it please?

[John O'Brian]

actually can you help me with this attached file? thanks!