# Solve a system of Differential Equations with EigenSystem DSolve MatrixExp?

Posted 2 months ago
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 In calculating a system of differential equations, I used 3 different methods: EigenSystem, DSolve and MatrixExp. DSolve and MatrixExp porduced the same answers but a different answers than EigenSystem and I don't understand why (See Attached). In all three cases, I used a default value of {1,1} for the values of the arbitrary constants. It appears that DSolve and MatrixExp simply dropped the negative exponent.I don't understand what I am overlooking.Thanks,Mitch Sandlin Attachments:
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Posted 2 months ago
 Hey Mitch, Apparently there is no problem in functionality of EigenSystem - it gives the correct solution. The problem was in specified initial conditions to the EigenSystem solution. In both DSolve and MatrixExp you specified that x[0]=1 and y[0]=1, which is analogous to the following in the EigenSystem solution: which results in {{c1 -> 0, c2 -> 1}} Thus, your final solution wont' have c1exp(1t) in it. (See attached workbook) Attachments:
Posted 2 months ago
 Thank you so much and I understand exactly what you are saying about actually calculating the values of c1 and c2. However I was actually trying to figure out a way to circumvent the necessity of performing the calculations for the following graphing reasons.My ultimate goal was to use Manipulate to dynamically load the values of c1 and c2 by dragging the cursor around the graph (see bottom of attached - CalcQuestion3). Do you have any suggestions on the best way to dynamically load the values of c1 and c2 to in conjunction with Manipulate? Attachments:
 They agree if c1 is zero...