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eq := {diff(u(t), t) = 3^(2/3)*a[1]*x(t)*z(t)-4^(2/3)*a[1]*x(t)*u(t), diff(x(t), t) = exp(-t)-2*a[1]*x(t)^2-2^(2/3)*a[1]*x(t)*y(t)-3^(2/3)*a[1]*x(t)*z(t), diff(y(t), t) = a[1]*x(t)^2-2^(2/3)*a[1]*x(t)*y(t), diff(z(t), t) = 2^(2/3)*a[1]*x(t)*y(t)-3^(2/3)*a[1]*x(t)*z(t)}
dsolve(eq,{x(t),y(t),z(t),u(t)})
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