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Kernel Crashing with NDSOlve


Hi all
i have this rather innocuous looking NDSolve command thats crashing the 
mathematica kernel,
NDSolve[{y'[x]==Min[s[x]+Sin[x],Cos[x]-s[x]],y[0]==0,s[x]==x^2},{y,s},{x,0,3}]

If i were to substitute s[x] in this equation with x^2 and then try solving, 
i get an answer, if i assign s[x] in advance and try solving it, i still get 
an answer but the nature of the algorithm followed by NDSolve doesnt allow 
it to take s[x] as a dependent variable and still have it occur inside the 
Min function! i find that weird!
Someone have an explanation??
thanks in advance!
Pradeep
p.s. also note the that the nature of my application is such that i'd like 
to solve this bunch of equations in a single shot without assignment 
statements hence i dont have use for the two approaches that i mentioned 
worked. 




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