请给出matlab实现以下问题的代码：取h = 0.2，分别用欧拉公式、隐式欧拉法和改进欧拉法解微分方程并比较精度。已知条件为：①当0<=x<=1时，y'=y-(2*x-y）②y(0)=1)③微分方程解析解为y = sqrt(1+2*x)

以下是matlab实现的代码：

% 定义微分方程dy/dx
dydx = @(x,y) y - (2*x - y);

% 定义取值范围和步长
x = 0:0.2:1;
h = 0.2;

% 定义初始值
y_euler = zeros(size(x));
y_implicit_euler = zeros(size(x));
y_improved_euler = zeros(size(x));
y_euler(1) = 1;
y_implicit_euler(1) = 1;
y_improved_euler(1) = 1;

% 欧拉公式
for i = 2:length(x)
    y_euler(i) = y_euler(i-1) + h * dydx(x(i-1), y_euler(i-1));
end

% 隐式欧拉法
for i = 2:length(x)
    f = @(y) y - y_implicit_euler(i-1) - h * dydx(x(i), y);
    y_implicit_euler(i) = fzero(f, y_implicit_euler(i-1));
end

% 改进欧拉法
for i = 2:length(x)
    y_predict = y_improved_euler(i-1) + h * dydx(x(i-1), y_improved_euler(i-1));
    f = @(y) y - y_improved_euler(i-1) - (h/2) * (dydx(x(i-1), y_improved_euler(i-1)) + dydx(x(i), y));
    y_improved_euler(i) = fzero(f, y_predict);
end

% 输出结果并绘图
y_exact = sqrt(1 + 2*x);
fprintf("欧拉公式误差：%f\n", max(abs(y_euler - y_exact)));
fprintf("隐式欧拉法误差：%f\n", max(abs(y_implicit_euler - y_exact)));
fprintf("改进欧拉法误差：%f\n", max(abs(y_improved_euler - y_exact)));

plot(x, y_exact, '-k', x, y_euler, '-r', x, y_implicit_euler, '-g', x, y_improved_euler, '-b');
legend('解析解', '欧拉公式', '隐式欧拉法', '改进欧拉法');
xlabel('x');
ylabel('y');

运行后，程序会输出三种方法的最大误差，并且绘制出解析解和三种方法的图像。