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I was trying to see what would happen if I let d=q in the following equation:

-((E^(-(3 + d + q - Sqrt[d^2 - d q + q^2]) t) (-3 d - 5 d^2 + 
   d^2 E^((3 + d + q - Sqrt[d^2 - d q + q^2]) t) + 
   3 d E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t + (3 + d + q - 
        Sqrt[d^2 - d q + q^2]) t) + 
   5 d^2 E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t + (3 + d + q - 
        Sqrt[d^2 - d q + q^2]) t) - 
   d^2 E^(2 Sqrt[d^2 - d q + q^2]
       t + (-3 - d - q - Sqrt[d^2 - d q + q^2]) t + 
     2 (3 + d + q - Sqrt[d^2 - d q + q^2]) t) - 5 d q - 3 d^2 q - 
   3 E^((3 + d + q - Sqrt[d^2 - d q + q^2]) t) q - 
   2 d E^((3 + d + q - Sqrt[d^2 - d q + q^2]) t) q + 
   5 d E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t + (3 + d + q - 
        Sqrt[d^2 - d q + q^2]) t) q + 
   3 d^2 E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t + (3 + d + q - 
        Sqrt[d^2 - d q + q^2]) t) q + 
   3 E^(2 Sqrt[d^2 - d q + q^2]
       t + (-3 - d - q - Sqrt[d^2 - d q + q^2]) t + 
     2 (3 + d + q - Sqrt[d^2 - d q + q^2]) t) q + 
   2 d E^(2 Sqrt[d^2 - d q + q^2]
       t + (-3 - d - q - Sqrt[d^2 - d q + q^2]) t + 
     2 (3 + d + q - Sqrt[d^2 - d q + q^2]) t) q + 
   3 E^((3 + d + q - Sqrt[d^2 - d q + q^2]) t) Sqrt[
    d^2 - d q + q^2] + 
   d E^((3 + d + q - Sqrt[d^2 - d q + q^2]) t) Sqrt[
    d^2 - d q + q^2] + 
   3 E^(2 Sqrt[d^2 - d q + q^2]
       t + (-3 - d - q - Sqrt[d^2 - d q + q^2]) t + 
     2 (3 + d + q - Sqrt[d^2 - d q + q^2]) t) Sqrt[
    d^2 - d q + q^2] + 
   d E^(2 Sqrt[d^2 - d q + q^2]
       t + (-3 - d - q - Sqrt[d^2 - d q + q^2]) t + 
     2 (3 + d + q - Sqrt[d^2 - d q + q^2]) t) Sqrt[
    d^2 - d q + q^2] + 18 d C[1] + 12 d^2 C[1] - 
   18 d E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t + (3 + d + q - 
        Sqrt[d^2 - d q + q^2]) t) C[1] - 
   12 d^2 E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t + (3 + d + q -
         Sqrt[d^2 - d q + q^2]) t) C[1] - 9 q C[1] + 6 d q C[1] + 
   6 d^2 q C[1] + 
   9 E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t + (3 + d + q - 
        Sqrt[d^2 - d q + q^2]) t) q C[1] - 
   6 d E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t + (3 + d + q - 
        Sqrt[d^2 - d q + q^2]) t) q C[1] - 
   6 d^2 E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t + (3 + d + q - 
        Sqrt[d^2 - d q + q^2]) t) q C[1] - 6 q^2 C[1] - 
   3 d q^2 C[1] + 
   6 E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t + (3 + d + q - 
        Sqrt[d^2 - d q + q^2]) t) q^2 C[1] + 
   3 d E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t + (3 + d + q - 
        Sqrt[d^2 - d q + q^2]) t) q^2 C[1] + 
   9 Sqrt[d^2 - d q + q^2] C[1] + 
   6 d Sqrt[d^2 - d q + q^2] C[1] + 
   9 E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t + (3 + d + q - 
        Sqrt[d^2 - d q + q^2]) t) Sqrt[d^2 - d q + q^2] C[1] + 
   6 d E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t + (3 + d + q - 
        Sqrt[d^2 - d q + q^2]) t) Sqrt[d^2 - d q + q^2] C[1] + 
   6 q Sqrt[d^2 - d q + q^2] C[1] + 
   3 d q Sqrt[d^2 - d q + q^2] C[1] + 
   6 E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t + (3 + d + q - 
        Sqrt[d^2 - d q + q^2]) t) q Sqrt[d^2 - d q + q^2] C[1] + 
   3 d E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t + (3 + d + q - 
        Sqrt[d^2 - d q + q^2]) t) q Sqrt[d^2 - d q + q^2] C[
    1]))/(2 Sqrt[
 d^2 - d q + 
  q^2] (-3 - d - q + Sqrt[d^2 - d q + q^2]) (3 + d + q + Sqrt[
   d^2 - d q + q^2])))

So I wrote in mathematica:

= let d = q in f (x) = ((E^(-(3 + d + q - Sqrt[d^2 - d q + q^2]) t) \
(-3 d - 
                        5 d^2 + d^2 E^((3 + d + q - Sqrt[d^2 - d q + \
q^2]) t) + 
                        3 d E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t \
+ (3 + d + q - Sqrt[
                                             d^2 - d q + q^2]) t) + 
                        5 d^2 E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) \
t + (3 + d + q - Sqrt[
                                             d^2 - d q + q^2]) t) - 
                        d^2 E^(2 Sqrt[d^2 - d q + q^2]
                                      t + (-3 - d - q - Sqrt[d^2 - d \
q + q^2]) t + 
                                  2 (3 + d + q - Sqrt[d^2 - d q + \
q^2]) t) - 5 d q - 3 d^2 q - 
                        3 E^((3 + d + q - Sqrt[d^2 - d q + q^2]) t) q \
- 
                        2 d E^((3 + d + q - Sqrt[d^2 - d q + q^2]) t) \
q + 
                        5 d E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t \
+ (3 + d + q - Sqrt[
                                             d^2 - d q + q^2]) t) q + \

                        3 d^2 E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) \
t + (3 + d + q - Sqrt[
                                             d^2 - d q + q^2]) t) q + \

                        3 E^(2 Sqrt[d^2 - d q + q^2]
                                      t + (-3 - d - q - Sqrt[d^2 - d \
q + q^2]) t + 
                                  2 (3 + d + q - Sqrt[d^2 - d q + \
q^2]) t) q + 
                        2 d E^(2 Sqrt[d^2 - d q + q^2]
                                      t + (-3 - d - q - Sqrt[d^2 - d \
q + q^2]) t + 
                                  2 (3 + d + q - Sqrt[d^2 - d q + \
q^2]) t) q + 
                        3 E^((3 + d + q - Sqrt[d^2 - d q + q^2]) t) \
Sqrt[d^2 - d q + q^2] + 
                        d E^((3 + d + q - Sqrt[d^2 - d q + q^2]) t) \
Sqrt[d^2 - d q + q^2] + 
                        3 E^(2 Sqrt[d^2 - d q + q^2]
                                      t + (-3 - d - q - Sqrt[d^2 - d \
q + q^2]) t + 
                                  2 (3 + d + q - Sqrt[d^2 - d q + \
q^2]) t) Sqrt[d^2 - d q + q^2] + 
                        d E^(2 Sqrt[d^2 - d q + q^2]
                                      t + (-3 - d - q - Sqrt[d^2 - d \
q + q^2]) t + 
                                  2 (3 + d + q - Sqrt[d^2 - d q + \
q^2]) t) Sqrt[d^2 - d q + q^2] + 
                        18 d C[1] + 12 d^2 C[1] - 
                        18 d E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) \
t + (3 + d + q - Sqrt[
                                             d^2 - d q + q^2]) t) \
C[1] - 
                        12 d^2 E^((-3 - d - q - Sqrt[d^2 - d q + \
q^2]) t + (3 + d + q - Sqrt[
                                             d^2 - d q + q^2]) t) \
C[1] - 9 q C[1] + 6 d q C[1] + 
                        6 d^2 q C[1] + 
                        9 E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t + \
(3 + d + q - Sqrt[
                                             d^2 - d q + q^2]) t) q \
C[1] - 
                        6 d E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t \
+ (3 + d + q - Sqrt[
                                             d^2 - d q + q^2]) t) q \
C[1] - 
                        6 d^2 E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) \
t + (3 + d + q - Sqrt[
                                             d^2 - d q + q^2]) t) q \
C[1] - 6 q^2 C[1] - 3 d q^2 C[1] + 
                        6 E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t + \
(3 + d + q - Sqrt[
                                             d^2 - d q + q^2]) t) q^2 \
C[1] + 
                        3 d E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t \
+ (3 + d + q - Sqrt[
                                             d^2 - d q + q^2]) t) q^2 \
C[1] + 9 Sqrt[d^2 - d q + q^2] C[1] + 
                        6 d Sqrt[d^2 - d q + q^2] C[1] + 
                        9 E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t + \
(3 + d + q - Sqrt[
                                             d^2 - d q + q^2]) t) \
Sqrt[d^2 - d q + q^2] C[1] + 
                        6 d E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t \
+ (3 + d + q - Sqrt[
                                             d^2 - d q + q^2]) t) \
Sqrt[d^2 - d q + q^2] C[1] + 
                        6 q Sqrt[d^2 - d q + q^2] C[1] + 3 d q \
Sqrt[d^2 - d q + q^2] C[1] + 
                        6 E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t + \
(3 + d + q - Sqrt[
                                             d^2 - d q + q^2]) t) q \
Sqrt[d^2 - d q + q^2] C[1] + 
                        3 d E^((-3 - d - q - Sqrt[d^2 - d q + q^2]) t \
+ (3 + d + q - Sqrt[
                                             d^2 - d q + q^2]) t) q \
Sqrt[d^2 - d q + q^2] C[1]))/(2 Sqrt[
                    d^2 - d q + 
                       q^2] (-3 - d - q + Sqrt[d^2 - d q + q^2]) (3 + \
d + q + Sqrt[
                          d^2 - d q + q^2])))`

I assumed the natural language processing could handle this one, but I got the errors

Request to knowledgebase server api.wolframalpha.com failed with error code 414.

Request to knowledgebase server api.wolframalpha.com failed with error code 414.

I looked around to get a sense of what this error meant, but I could not find any details googling or searching on SE.

What does the error mean? Can Mathematica language processing handle these types of operations? If so, how should I phrase my requests to Mathematica?How would you do this without natural language processing in Mathematica?

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1 Answer 1

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You have defined f(x) = stuff but there is no x in the stuff. Instead, define

f[d_,q_]:= stuff

Then you can evaluate:

f[1,1]
1/48 E^(-4 t) (-16 + 16 E^(-2 t) + 8 E^(4 t) + 48 C[1])

or

f[x, x] // FullSimplify

to see what happens in general.

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  • $\begingroup$ Thank you for your help! $\endgroup$ Commented Jul 27, 2019 at 11:33

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