# Using FindRoot as a nonlinear function inside NDSolve [duplicate]

I am solving a nonlinear ODE using NDSolve, and one of the terms is an implicit nonlinear function of the dependent variable, for which I am using FindRoot. Here's a trivial example:

y[x_] := y /. FindRoot[Exp[Log[y]] == x, {y, 1}];


I can plot this function, and it gives a straight line y= x, but when I put the function into NDSolve, I get an error message.

s = NDSolve[{h'[t] == -y[h[t]], h[0] == 1}, h, {t, 0, 2}]


and then

Plot[Evaluate[h[t]/.s],{t,0,2}]


If the function y[h[t]] were working, the solution would be h[t]=Exp[-t]. Does every term in NDSolve have to be an explicit function? Is there a way around this?

## marked as duplicate by Chris K, m_goldberg, halirutan♦, Carl Woll, CoolwaterJan 22 '18 at 19:16

• Functions that make use of numeric techniques should have their arguments restricted to numeric values: y[x_?NumericQ] := ... – Bob Hanlon Jan 21 '18 at 21:44
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• – Michael E2 Jan 21 '18 at 22:45
• Why not use NDSolve[{Exp[Log[-h'[t]]] == h[t], h[0]==1}, h, {t, 0, 2}] instead? – Carl Woll Jan 22 '18 at 16:29

y[x_?NumericQ] := y /. FindRoot[Exp[Log[y]] == x, {y, 1}];