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Transforming an initial condition of a solved ODE into a new


I solved a two-variable(x[t],y[t]) second-order ODE. Now I wish to transform one initial condition of the problem (x[0]) into a variable, so that I can compute the following (which I give here symbolically to convey my intention):

1) Plot[y'[tmax][x[0]],{x[0],0,100}]
2) NIntegrate[y'[tmax][x[0]],{x[0],0,100}]

How can this be done?

Thank you


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