#This code is SageMath to compute an ODE explicitly
#Run this with CoCalc on its web based cloud platform
#Visit webpage for the computing outcome:
#    https://cocalc.com/share/3e846d30-3d24-467c-a0d8-58549b3cf8f6/2018-06-21-155129.ipynb?viewer=share

x, a = var('x', 'a')
u = function('u')(x)

#Setup ODE parameterized by a
de = 1/2*a^2*diff(u,x,2) + diff(u, x) - u + 1 == 0
show(de)

#Solve for ODE with zero boundary value
f = desolve(de, dvar = u, ivar = x, ics = [0, 0, 1, 0]);
show(f)