I want to prove:
Let x:y denote the partial derivative of x with respect to y.
Let u,v be functions of x,t.
u,v --> 0 as x goes to infinity.
u:t=u:xx for x,t>0
u(x,0) = 0
u(0,t)=f(t)
and
v:t=v:xx for x,t>0
v(x,0)=0
v(0,t)=1
then
u(x,t)=INT(t,0){f(t-s)*v:t(x,s)}ds...