Question: System of differential equations and algebraic equations

Hello, how can i solve these equations

eq[1]:=a'[1](t)*p[1](x)+b*a[1](t)*p[1](x)

eq[2]:=a'[2](t)*p[2](x)+b*a[2](t)*p[2](x)

eq[3]:=a'[3](t)*p[3](x)+b*a[3](t)*p[3](x)

eq[4]:=c[1]*a[1](t)+c[2]a[2](t)+c[3]a[3](t)-q(t)

eq[5]:=d[1]*a[1](t)+d[2]a[2](t)+d[3]a[3](t)-p(t),

where p[i](x) , c[i] , d[i] , q(t) and p(t) are known functions?

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