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In such cases it can be useful to introduce auxiliary variables at the input of the integrators. For the given diagram you could use a signal $u(t)$ at the input of the second integrator. The equation for its Laplace transform $U(s)$ becomes $$U(s)=\frac{1}{s}\big[X(s)-bY(s)\big]-aY(s)\tag{1}$$ You need another equation relating $U(s)$ to $Y(s)$, but that ...