#definimos nuestras variables
x,u,v,w = var("x,u,v,w")
eqn1 = u + cos(x)*v + sin(x)*w == 0
eqn2 = -sin(x)*v + cos(x)*w == 0
eqn3 = -cos(x)*v - sin(x)*w == sec(x)
sol = solve([eqn1, eqn2, eqn3], [u,v,w], solution_dict=True)
print sol
print sol[0][u]
u(x)=sol[0][u]
show(u)
U(x)=u.integrate(x)
show(U)
v(x)=sol[0][v]
show(v)
v(x)=v.simplify_full()
show(v)
V(x)=v.integrate(x)
show(V)
w(x)=sol[0][w]
show(w)
w(x)=w.simplify_full()
show(w)
W(x)=w.integrate(x)
show(W)