- #1

member 428835

The following is a simple ODE I'm solving via DSolve. However, the solution, which I call uEven, does not work as a typical function. Note the last two lines are different. Does anyone know how to fix this, so that I can differentiate and integrate the output of this ODE without copy-pasting?

Ideally I'd like the solution to adapt to different input constants shown at the top. Any help much appreciated!

Code:

```
L = 0.005; (* HALF CHANNEL LENGTH (m) *)
\[Sigma] = 0.07; (* \
SURFACE TENSION (N / m) *)
\[Rho] = 1000; (* LIQUID \
DENSITY (kg / m^3) *)
g = 9.8; (* GRAVITY ACCELERATION (m / \
s^2) *)
\[Alpha] =
70 \[Pi]/180; (* STATIC CONTACT ANGLE (rad) *)
l = \
Sqrt[\[Sigma]/(\[Rho] g)]; (* CAPILLARY LENGTH SCALE (m) *)
b = (\
\[Rho] g l^2)/\[Sigma]; (* BOND NUMBER *)
\[CapitalGamma][x_,
l_, \[Alpha]_, L_] :=
l Cot[\[Alpha]] Exp[L ( x - 1)/l](* EQUILIBRIUM HEIGHT (m) *)
uEven[x, b, l, \[Alpha], L] =
y[x] /. First@
DSolve[{-y''[
x] + (b Cos[\[Alpha]] - \[CapitalGamma][x, l, \[Alpha],
L]^2) y[x] == 0, y'[0] == 0}, y, x];
uEven[x, b, l, \[Alpha], L]
uEven[y, b, l, \[Alpha], L]
```