求解这个常微分方程组。
初始条件为
其中ε取0.01，a是有上限的参数，求解方程的目的其实是找出a的临界值。
syms y(t) for i = [0:0.5:1.5,1.763] %1.763是临界值eqn = diff(diff(y,2)*y^3) == i*diff(y,2)^2*y;%化三阶方程为一阶V = odeToVectorField(eqn);M = matlabFunction(V,'vars',{'t','Y'});e = 0.01;% 坐标范围和初始条件interval = [0 2/e];yInit = [1/e -1 e^3];ySol = ode45(M,interval,yInit);tValues = linspace(0,2/e,1000);yValues = deval(ySol,tValues,1);pValues = deval(ySol,tValues,3)./yValues.^2;vValues = yValues.^3;plot(tValues,yValues)hold onendylim([-10 100])xlabel('$\hat{t}$','interpreter','latex');ylabel('$\hat{R}$','interpreter','latex');text(60,80,'\epsilon=0.01','FontName','Times New Roman','FontSize',15)lgd = legend(num2str(0),num2str(0.5),num2str(1),num2str(1.5),num2str(1.763));title(lgd,'\xi_n_o_\alpha')set(gca,'LineWidth',2)set(findall(gcf,'type','line'),'linewidth',2)set(gca,'FontName','Times New Roman','FontSize',15)
