The department of the differential equations has been opened for the first time in 1939 with Prof. K.P.Persidsky as the head. However, with the beginning of the Great Patriotic War the department was closed.
The further history of the department was connected with Feodor Dmitrievich Gakhov who has graduated from Kazan University in 1930 and completed his postgraduate studies in 1937. In his PhD thesis Gakhov gave the full solution of a Riemann boundary-value problem, which was studied earlier by such outstanding mathematicians, as Hilbert, Plemelj, Carleman, and Privalov. This result laid the foundation of further investigations in the USSR for several decades. F.D.Gakhov in 1949 headed again a re-opened department of differential equations. This period of his life was very productive from the scientific point of view. Eleven PhD theses were defended under the supervision of Prof. Gakhov during 1947-1953. Four of these 11 became later doctors of sciences.
After Gakhov’s leaving for Rostov University an associate professor Sergey Nikolaevich Andrianov was invited as a department, who under the influence of Gakhov investigated the existence, uniqueness, and univalence solutions of inverse boundary-value problems.
In 1959, after S.N.Andrianov's premature demise, the department was headed by Ljubov Ivanovna Chibrikova (one of the first Gakhov‘s students). In 1962 she became the first woman in Kazan University history who defended the thesis for a doctor's degree in mathematics. She developed the foundations of the theory of Riemann’s boundary-value problems on compact of Riemann surfaces and discovered deep connections of studied problems with a classical problem of Jacobi’s inversion problem. Prof. Chibrikova supervised about 30 PhD theses, eight of her students became doctors of sciences. She was the department of differential equations until 1991 when she transferred this post to professor Valentin Ivanovich Zhegalov.
Scientific interests of Prof. Zhegalov are connected with the theory of differential equations of a mixed type. He studied the problems with a shift for the equations of a mixed type, and also gave a new version of Riemann’s method for solution of hyperbolic equations which in multidimensional cases is more constructive than the classical one. During last years, together with his post-graduate students he was developing expansion of the suggested method to multidimensional analogs of the pseudo-parabolic equations.
Since 1999 professor Yu.V.Obnosov has been the department (he is a former student of L.I.Chibrikova as well as Zhegalov). Research conducted by him is in the field of the theory of a generalized Riemann boundary-value problem, with modeling of physical processes in heterogeneous media.