$$\begin{array}{rl}& {\dot{v}}_l=a_l\\ & {\dot{v}}_f=?\frac{0.1+5?v_f+0.25?v_f^2}{m}\\ & \dot{D}=v_l?v_f\end{array}$$

%% Solve Differential Equations % Author: Zhao-Jichao % Date: 2021-07-18 clear clc%% Initial Parameters % Variable initial values vl0 = 1; vf0 = 2; D0 = 3;%% Solve ODE % Time parameters tBegin = 0; tFinal = 10; in = [vl0 vf0 D0]'; [t, out] = ode45(@odeFun, [tBegin, tFinal], in);%% Draw Results subplot(2,2,1) plot(t,out(:,1), t,out(:,2), t,out(:,3), 'linewidth',1.5); legend('v_l', 'v_f', 'D'); grid on;subplot(2,2,2) plot(t,out(:,1), 'linewidth',1.5); hold on ; legend('v_l'); grid on;subplot(2,2,3) plot(t,out(:,2), 'linewidth',1.5); hold on ; legend('v_f'); grid on;subplot(2,2,4) plot(t,out(:,3), 'linewidth',1.5); hold on ; legend('D'); grid on;%% Ode SubFunction function out = odeFun(~, in)vl = in(1,:);vf = in(2,:);D = in(3,:);al = 1;m = 1;% Set up differential relationsdvl = al;dvf = -(0.1 + 5*vf + 0.25*vf^2) / (m);dD = vl - vf;out = [dvl; dvf; dD]; end

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