@sunit 

''The resource you are looking for might have been removed, had its name changed, or is temporarily unavailable.''

Please paste your code.

Could you please paste your try?

You can check here pdsolve for details.

@Carl Love 

Thanks for pointing out.

@Preben Alsholm 

I tried twice to link the two but couldn't succeed.

I am confused about this "The boundary conditions for U are assuming that L > 0."

@Carl Love 

once we have T(z) then resubing z=P/L^2*exp(-L*x) will give T(x).

I am looking for T(x) in a compact form in terms of GAMMA function.

@Preben Alsholm 

I have simplified the problem. Something like this

ODE:=(diff(T(x), x, x))+P*(S+a*(1-exp(-L*x))/L)*(diff(T(x), x))=0;

bcs:=T(0)=1,T(infinit)=0;

where P, S, L are all constants.

let assume that 

z=P/L^2*exp(-L*x);

subing z into the ode, we can have

ode1:=diff(T(z), z$2)+(1+z*a-P)*(diff(T(z), z)) = 0;

bcs1:=T(P/L^2)=1,T(0)=0;

Is it possible to find a closed form solution?

@Preben Alsholm 

Plotting takes too much time

L:=(S-sqrt(S^2+4*alpha*epsilon))/(2*epsilon);:

A1:=3*R*P/(epsilon2*(3*R+4));

A2:=3*n*R*P/(epsilon2*(3*R+4));

ODE:=diff(T(eta),eta$2)+A1*(S-1/L+1/L*exp(-L*eta))*diff(T(eta),eta)+A2*T(eta)=0;

bcs:=T(0)=1,T(inf)=0;

sol:=dsolve({ODE,bcs}):
plot(eval(rhs(sol),{epsilon=.01,epsilon2=.1,alpha=5,R=1,n=1,P=6,S=1,inf=5}),eta=0..5);

@Preben Alsholm 

L:=(S-sqrt(S^2+4*alpha*epsilon))/(2*epsilon);:

A1:=3*R*P/(epsilon2*(3*R+4));

A2:=3*n*R*P/(epsilon2*(3*R+4));

ODE:=diff(T(eta),eta$2)+A1*(S-1/L+1/L*exp(-L*eta))*diff(T(eta),eta)+A2*T(eta)=0;

bcs:=T(0)=1,T(infinity)=0;

alpha:=-5:R:=1:n:=1:P:=6:S:=1:

simplify(dsolve({ODE,bcs})):

@Preben Alsholm that's right!!! how to avoid that?

@Markiyan Hirnyk 

404 - File or directory not found.

The resource you are looking for might have been removed, had its name changed, or is temporarily unavailable.

@Markiyan Hirnyk Unable to download the sheet

@Kitonum Thanks,

For some value of the different constants I get imaginary results.

Is it possible to get the solution in some other special function not the Kummer one's? 

Adding to Georgios's 

style will be helpful to differentiate 

restart:with(plots):
p1:=pointplot({seq([n, sin((1/10)*n)], n = 0 .. 30)},color=red,style=line):

p2:=pointplot({seq([n, cos((1/10)*n)], n = 0 .. 30)},color=green,style=point):

display(p1,p2);

@acer 

F12 := -(1/2*(S+sqrt(S^2+4*alpha)))*alpha:
F22 := (1/2*(-S+sqrt(S^2+4*alpha)))*alpha:
solve(F12=F22,alpha);

plottools:-transform((x,y,z)->[y,x,z])(
   plot3d({F12,F22}, alpha=max(-1,-S^2/4)..0, S=-20..20));

The op command is not giving me data for the above 3d plot.