This problem book contains exercises for courses in differential equations at technical institutes. Particular attention is given to questions which are not sufficiently treated in the available textbooks and which, as is shown by experience, are poorly understood by students. Worked out in detail are the method of isoclines for equations of the first and the second order, problems in finding orthogonal trajectories, linear dependence and linear independence of systems of functions. The book indudes a large number of problems in solving linear equations with constant and variable coefficients, problems in Lyapunov stability, in applying the operator method to solving differential equations and systems. Some new sections have been introduced: the method of successive approximations, particular solutions of differential equations, and equations with a small parameter of the derivative. The section devoted to the use of series in solving differential equations has been enlarged, some revisions have been made, and errors and misprints noticed in the previous edition corrected.