# x/.NSolve[f==g,x] does not work when f or g is the output of NDSolve!

I have been trying to put Points at the intersection of two curves, one of which is the ouput of a differential equation solved with NDSolve. The output being an Interpolation, NSolve cannot find the intersection coordinates.

• NSolve[] wouldn't be up to the task here, as it's mostly intended for algebraic equations. Why not mention the particular "curves" whose intersections you seek? Maybe the differential equation too, while you're at it... – J. M. will be back soon Nov 3 '12 at 16:46
• The docs do mention that "NSolve deals primarily with linear and polynomial equations." Maybe you should try with FindRoot, but that locates one root at a time as it's a fully numerical function. – acl Nov 3 '12 at 16:49
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I would use FindRoot in this case. For example:

solution1=NDSolve[{y'[x]==2y[x],y==1},y[x],{x,-1,1}][[1,1,2]];
solution2=NDSolve[{y'[x]==-3y[x],y==3},y[x],{x,-1,1}][[1,1,2]];
Plot[{solution1,solution2,solution1-solution2},{x,-1,1}]
FindRoot[solution1-solution2,{x,0}]


With the results: • I could not get FindRoot to work when one functionF"f" is the result of NDSolve and the other function "g"is – Jean-Pierre Raynauld Nov 3 '12 at 21:18
• I could not get FindRoot to work when "f" is the output of NDSolve and "g" is a simple function like y=2x! – Jean-Pierre Raynauld Nov 3 '12 at 21:20
• @Jean, as you've been told previously, edit your question to include the Mathematica code you already have, including the NDSolve[]` bits. – J. M. will be back soon Nov 3 '12 at 23:54