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The systems of differential equations whose solutions exactly coincide with Bethe ansatz solutions for generalized Gaudin models are constructed. These equations are called the generalized spectral ${(}^1)$ Riccati equations, because the simplest equation of this class has a standard Riccatian form. The general form of these equations is $R_{n_i}[z_1\left(\lambda \right),...,z_r\left(\lambda \right)]=c_{n_i}\left(\lambda \right)$, i=1,..., r, where $R_{n_i}$ denote some homogeneous polynomials of degrees $n_i$ constructed from functional variables $z_i\left(\lambda \right)$ and their derivatives. It is assumed that $deg{\partial }^k{z}_i\left(\lambda \right)=k+1$. The problem...