DSolve output - understanding how to extract result

Question

I'm a little confused with how to use the output from DSolve. The following works

s = DSolve[{y'[x] == x, y[0] == 0}, y[x], x];
Plot[y[x] /. s, {x, 1, 10}]

but I don't understand how it works. I am familiar with /. a -> b which will replace a with b, but I don't get what y[x] /. s is doing?

Dr. belisarius · Accepted Answer · 2013-01-26 01:25:38Z

2

Dsolve[], like Solve[] (but unlike Resolve[]) returns replacement rules. You are replacing the value of y[]returned by your solve command

answered Jan 26, 2013 at 1:25

Dr. belisarius

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$\begingroup$ Thanks. I see whats going on. I can declare a mapping such as map = {a->b}; then i can use this mapping variable in a any ReplaceAll command i.e a /. map or {a,a} /. map. $\endgroup$
– David McHarg
Jan 26, 2013 at 2:10
$\begingroup$ @David Yes. Replacement rules (term rewriting) are very important in Mathematica. $\endgroup$
– Dr. belisarius
Jan 26, 2013 at 9:25

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