Hello,

I have a system of equations which I try to solve with the command NDSolve. Probably, I am making a mistake concerning syntax but I could not find since many hours.

Here is my code ;

u[c_] := (c^(1 - \[Sigma]) - 1)/(1 - \[Sigma])
h[s_] := (2 hbar)/(1 + Exp[\[Eta] (1 - s/sbar)])
d[s_] := (b s^2)/2
mit[m_] := m^\[Alpha]
r[m_, s_] := 
pricemit - (D[u[c], c] /. c -> (\[Chi] s + mit[m])/\[Beta]) D[mit[m],m]\[Psi][k_] := \[Omega] + (1 - \[Omega]) Exp[-\[Gamma] k]
co[a_] := x  (a^2)/2
adap[k_, s_] := (\[Rho] + h[s] + \[Delta]) co'[\[Delta] k] + \[Psi]'[k] d[s]

The calibration I use ;

paramFinal2 = {\[Sigma] -> 2.1, \[Rho] -> 0.01, sbar -> 101, \[Eta] -> 5.8, hbar -> 0.04, b -> 0.0001, \[Gamma] -> 0.6, \[Chi] -> 0.025, \[Omega] -> 0.185, \[Delta] -> 0.015, x -> 0.14, \[Beta] -> 0.8, pricemit -> 0.006, \[Alpha] -> 0.33};

For initial conditions ;

{aa} = {0.093944}
{mm} = {122.833}
{cc} = {6.8795}
{kk} = {6.26293}
{ss} = {24.4696}

The system is composed by 5 equations that I define as follows ;

dec1 = c'[t] == u'[c[t]]/u''[c[t]] (-\[Chi] - (\[Rho] + h[s[t]]) + h'[s[t]]/([Rho] + h[s[t]]) (1/(u'[c[t]]/\[Beta]) (u[c[t]] - \[Psi][k[t]] d[s[t]] -co[a[t]] - pricemit mit[m[t]])) + (\[Psi][k[t]]  d'[s[t]])/(u'[c[t]]/\[Beta]) -h'[s[t]]/(\[Rho] + h[s[t]]) (\[Beta] c[t] - \[Chi] s[t] - mit[m[t]]) + (h'[s[t]] co'[a[t]] )/((\[Rho] + h[s[t]]) u'[c[t]]/\[Beta]) (a[t] - \[Delta] k[t]));

dea1 = a'[t] == - (co'[a[t]]/co''[a[t]] (\[Rho] + h[s[t]] + \[Psi]'[k[t]]/co'[a[t]] + \[Delta]));

des1 = s'[t] ==   -(\[Beta] c[t] - \[Chi] s[t] - mit[m[t]]);

dek1 = k'[t] == -(a[t] - \[Delta] k[t]);

dem1 = m'[t] == -(mit'[m[t]]/mit''[m[t]] (-\[Chi] - (\[Rho] + h[s[t]]) +h'[s[t]]/(\[Rho] + h[s[t]]) (1/(u'[c[t]]/\[Beta]) (u[c[t]] - \[Psi][k[t]] d[s[t]] - co[a[t]] - pricemit mit[m[t]])) + (\[Psi][k[t]]  d'[s[t]])/(u'[c[t]]/\[Beta]) - h'[s[t]]/(\[Rho] + h[s[t]]) (\[Beta] c[t] - \[Chi] s[t] - mit[m[t]]) + (h'[s[t]] co'[a[t]] )/((\[Rho] + h[s[t]]) u'[c[t]]/\[Beta]) (a[t] - \[Delta] k[t])));

I use NDSolve as follows ;

nbsa = NDSolve[{dec1 /. paramFinal2, des1 /. paramFinal2, dea1 /. paramFinal2, dek1 /. paramFinal2, dem1 /. paramFinal2, c[0] ==  cc (1 - 10^-10), s[0] == ss (1 - 10^-5), a[0] == aa (1 - 10^-5), k[0] == kk (1 + 10^-2), m[0] == mm (1 -10^-2)}, {c[t], s[t], k[t], a[t], m[t]}, {t, 0, 350}]

Mathematica always gives me the error

NDSolve::deqn: Equation or list of equations expected instead of True in the first argument

What am I missing on this code ? Thanks so much in advance for all hints or suggestions.