About Aditya’s question: I have two books, one is by Bitsadze, the other by Kolmogorov, Tichonov titled something like PDE in Physics, or Equations of mathematical physics, and another book of the Course by Smirnov devoted to PDEs. To my knowledge other books are: Krasnov M., A book of problems in ordinary differential equations, and Mikhailov V., PDEs.