Bachelors and graduate students are offered in the course of teaching computational informatics, the ability to solve nonstandard mathematical problems, which, as a rule, are not included in the content of teaching computational informatics. The article aimed to analyze the application effectiveness of non-standard mathematical problems in the course of teaching computational informatics, elaboration of constructive computational solution algorithms of inverse problems for differential equations, during which the bachelors and graduate students develop own professional competencies. The research conducted a review of previous literature on the topic. Formulation of the inverse problem for differential equations for the investigation of which the computational mathematics finite difference methods are applied, is presented. In the course of investigation, it was revealed that at elaborating the constructive computational algorithms of its solution, the bachelors and graduate students develop not only fundamental knowledge in the field of applied and computational mathematics, computational informatics methods, but also develop the professional competences, including computational thinking.