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# How do I NIntegrate solutions to Differential Equations?

Posted 2 years ago
 How do I use NIntegrate solutions to Differential Equations? IntegratedDifferenceFunction[I_, O_] := NIntegrate[I[U] - O[U], {U, 0, 2*Pi}] m = DSolve[y''[x] + y[x] == 0, y[x], x] n = DSolve[y''[x] + y'[x] == 0, y[x], x] IntegratedDifferenceFunction[m, n]  I want to compute the difference between two Ordinary Differential Equation Solutions from 0 to 2*Pi, It can be any ODE's. Is there also a way to apply the function for Numerical Solutions that were solved using NDSolve?  m = NDSolve[y''[x] + y[x] == 0, y[x], {x,0,2*Pi}] n = NDSolve[y''[x] + y'[x] == 0, y[x], {x,0,2*Pi}] 
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Posted 2 years ago
 Do you perhaps mean something like this? IntegratedDifferenceFunction[fi_, fo_] := NIntegrate[fi - fo, {x, 0, 2*Pi}] g1 = DSolve[{y''[x] + y[x] == 0, y[0] == .8, y'[0] == -.2}, y, x] g2 = DSolve[{y''[x] + y'[x] == 0, y[0] == .8, y'[0] == -.2}, y, x] fgi = y[x] /. g1[[1, 1]] fgo = y[x] /. g2[[1, 1]] IntegratedDifferenceFunction[fgi, fgo] 
Posted 2 years ago