Final answer:
The student's question deals with solving various types of differential equations, not a physics problem related to velocities. There appears to be a mix-up in the provided information, which is not applicable to the mathematics question at hand.
Step-by-step explanation:
The student's question involves solving differential equations by using the method of separation of variables.
However, the provided information is not applicable or correct for the questions a), b), c), and d), as it seems to be referring to an unrelated physics problem involving velocities and relativistic effects.
The equations provided in the original question represent different types of partial differential equations and should be solved using appropriate mathematical techniques distinct to each equation's characteristics.