How Can I Extract Function Expressions from a DSolve Solution in Mathematica?

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SUMMARY

The discussion centers on extracting function expressions from a DSolve solution in Mathematica. The user encountered an issue where substituting values from a solution array resulted in retaining the function structure instead of the desired expressions. The solution was achieved by correctly applying replacement rules to extract the expressions directly, allowing the user to construct a matrix with the desired function outputs. The final matrix was successfully defined with the expressions extracted from the DSolve output.

PREREQUISITES
  • Familiarity with Mathematica syntax and functions
  • Understanding of DSolve for solving differential equations
  • Knowledge of function definitions in Mathematica
  • Basic matrix operations in Mathematica
NEXT STEPS
  • Explore advanced features of DSolve in Mathematica
  • Learn about replacement rules and their applications in Mathematica
  • Investigate matrix manipulation techniques in Mathematica
  • Study function extraction methods from complex data structures in Mathematica
USEFUL FOR

Mathematica users, mathematicians, and engineers who are solving differential equations and need to manipulate function outputs effectively.

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I have a very simple issue with Mathematica, but I can't seem to find an answer for it.

I solved an equation with DSolve, and I got a result as an array of the following type:

Solution = { A11 -> Function[ {t} , expression1] , A22 ->Function[ {t}, expression 2] , etc }

Now I want to define a matrix with elements {{A11, A12},{A21, A22}} and to give these elements the values for expression1, expression 2, etc, essentially to put those functions in a matrix:

{{ expression 1, expression 2},{ expression 3, expression 4}}

What I tried so far is to use R11 = {A11} /. Solution[[1]] , but it gives R11 the value Function [ {t} , expression 1] and not expression 1.

How can I solve this issue?
 
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Solved. Thanks.
 

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