Dear Gianluca,
I want to solve eq13 and eq15 rather than only eq13.
I ran your codes and it didn't work well.
In[15]:= eq12 = (cinf \[Theta]c \[Lambda])/(s + \[Theta]c) - (E^((lh -
x)/Sqrt[Dc] Sqrt[s + \[Theta]c]) F1 Sqrt[Dc] \[Lambda])/
Sqrt[(s + \[Theta]c)] /. {Sqrt[Dc] F1 \[Lambda] -> A1,
cinf \[Theta]c \[Lambda] -> A2}
Out[15]= A2/(s + \[Theta]c) - (
A1 E^(((lh - x) Sqrt[s + \[Theta]c])/Sqrt[Dc]))/Sqrt[s + \[Theta]c]
In[16]:= eq13 = s*q[x, s] - Dp*D[q[x, s], {x, 2}] - pinf + eq12 == 0
Out[16]= -pinf + A2/(s + \[Theta]c) - (
A1 E^(((lh - x) Sqrt[s + \[Theta]c])/Sqrt[Dc]))/Sqrt[
s + \[Theta]c] + s q[x, s] - Dp
\!\(\*SuperscriptBox[\(q\), \*
TagBox[
RowBox[{"(",
RowBox[{"2", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[x, s] == 0
In[17]:= sol =
Assuming[(lh - x) < 0 && s > 0 && s + \[Theta]c > 0 && Dp > 0 &&
Dc > 0 && \[Alpha]1 > 0, DSolveValue[eq13, q, {x, s}]]
Out[17]= DSolveValue[-pinf + A2/(s + \[Theta]c) - (
A1 E^(((lh - x) Sqrt[s + \[Theta]c])/Sqrt[Dc]))/Sqrt[
s + \[Theta]c] + s q[x, s] - Dp
\!\(\*SuperscriptBox[\(q\), \*
TagBox[
RowBox[{"(",
RowBox[{"2", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[x, s] == 0, q, {x, s}]
In[18]:= Collect[
Expand@sol[x, s], {E^(Sqrt[s/Dp] x), E^(-Sqrt[(s/Dp)] x),
E^((lh - x) Sqrt[(s + \[Theta]c)/Dc])}, Simplify@*ExpandDenominator]
\:6B63\:5728\:8BA1\:7B97In[18]:= Syntax::sntxf: "Simplify@" cannot be followed by "*ExpandDenominator".
\:6B63\:5728\:8BA1\:7B97In[18]:= Syntax::tsntxi: "Simplify@" is incomplete; more input is needed.
\:6B63\:5728\:8BA1\:7B97In[18]:= Syntax::sntxi: Incomplete expression; more input is needed .