The discussion revolves around the process of reduction of order in solving second order differential equations, specifically addressing the treatment of constants in the general solution. Participants explore the implications of dropping or substituting constants during the solution process.
Participants express differing views on the treatment of constants, with no consensus reached regarding the necessity or implications of dropping constants in the solution process.
The discussion highlights assumptions about the role of arbitrary constants in the general solution of second order differential equations, but does not resolve the implications of these assumptions.
Because keeping ##k## is the same thing as adjusting the value of the arbitrary constant ##c_1## in the general solution?chwala said:
Thanks noted...was wondering why they substituted for the constant ##c=-3## and dropped the other constant ##k##. The constant ##c## was not dropped as indicated rather a value was assigned to it. .renormalize said:
Just like keeping ##k## amounts to redefining ##c_1##, wouldn't keeping ##-c/3## simply adjust the value of the arbitrary constant ##c_2##? These are the types of simplifications that come naturally once you're practiced enough solving differential questions. When solving a 2nd-order ODE, as long as you're left in the end with two arbitrary constants, you know you've found the general solution.chwala said: