%%
%1.求y=0的结果
syms x
y = x*sin(x)-x;
solve(y, x)
cos(x)
%cos(x)的平方
syms x
solve('(cos(x))^2-(sin(x))^2', x)
%%
%2.二元一次方程式
syms x y
eq1 = x - 2*y - 5;
eq2 = x + y - 6;
A = solve(eq1,eq2,x,y)

%%
%3.未知ab求方程结果
syms x a b
solve('a*x^2-b')
%求b的关系
syms x a b
solve('a*x^2-b', 'b')

%%
%4.syms求积分
syms x
y = 4*x^5; 
yprime = diff(y)

%%
%5.符号集成
syms x; y = x^2*exp(x);
z = int(y); z = z-subs(z, x, 0)

%%
%6.fsolve()数值根求解器
f2 = @(x) (1.2*x+0.3+x*sin(x));
fsolve(f2,0)

%%
%7fzero()数值根求解器
f=@(x)x.^2
fzero(f,0.1)%必须与x轴相交
fsolve(f,0)

%%
%8迭代次数容错
f=@(x)x.^2
options=optimset('MaxIter',1e3,'TolFun',1e-10);
fsolve(f,0.1,options)
fzero(f,0.1,options)

%%
%9递归
function output = fact(n)
% fact recursively finds n!
if n==1
output = 1;
else
output = n * fact(n-1);
end
end