用matlab编程显示欧拉法解决如下问题dudt = −4u + 6v u0 = 1dvdt = 3u − 7v v0 = 20t1

% 欧拉法解决du/dt = -4u + 6v, u(0) = 1 % dv/dt = 3u - 7v, v(0) = 2, (0<t<1)

% 设置步长和时间范围 h = 0.01; t = 0:h:1;

% 初始化u和v u = zeros(length(t),1); v = zeros(length(t),1); u(1) = 1; v(1) = 2;

% 欧拉法迭代 for i=2:length(t) u(i) = u(i-1) + h*(-4u(i-1)+6v(i-1)); v(i) = v(i-1) + h*(3u(i-1)-7v(i-1)); end

% 绘制图像 plot(t,u,'r',t,v,'b'); xlabel('t'); legend('u(t)','v(t)'); title('Euler method for du/dt = -4u + 6v, u(0) = 1,dv/dt = 3u - 7v, v(0) = 2, (0<t<1)');