1)
x=var('x')
solve (x^6-9*x^5+10*x^4+18*x^3+49*x^2+135*x+84==0,x)
2)
x=var('x')
solve (x^3-5* x^2+8* x-40==0, x)
3)
x=var('x')
solve(cos(x)==x,x)
find_root(cos(x)==x,0,pi)
4)
integral(x*sin(x),x)
-x*cos(x) + sin(x)
5)
integral(e^(1/(x^2)),x,-2,4)

6)
diff(sqrt(x^2*sin(x+2)),x)
7)
diff((x*e^(cos(x)))^(3),x)
8)
x,y=var('x,y')
f=x^2+sin(x*y)-y
f.diff(y)

9)
A=matrix([[1,-4,7],[14,6,8],[-4,-1,2]]);A
B=matrix([[2,3,9],[-1,17,6],[0,5,-7]]);B
A*B
10)
A.determinant()
11)
B^(-1)
12)
x=var('x')
u=function('u')(x)
show(desolve(diff(u,x,2)-x*diff(u,x)+u==0,u,contrib_ode=True,show_method=True))