The plane isothermal motions of an ideal gas without expansions

A general solution of the equations of plane isothermal motions of an ideal gas without expansions is obtained. A method of reducing the overdetermined system of differential equations to an involution is proposed, which consists of obtaining integrable relations. All representations of the solution in time are obtained: polynomial, harmonic and biharmonic, and representations of linearly and exponentially increasing harmonics. All the representations give solutions of the overdetermined system, among which there are all the solutions with linear velocity fields, obtained by Ovsyannikov.