The discussion revolves around solving a differential equation of the form y(x) = C1sin(2x) + C2cos(2x) with specific initial conditions. Participants are trying to understand how to derive the relationship between constants C1 and C2 based on the given condition y(∏/8) = 0.
Some participants have offered guidance on manipulating the initial condition equation, while others are exploring the implications of their assumptions about the constants. Multiple interpretations of the problem are being discussed, particularly regarding the relationships between C1 and C2.
There is a mention of an additional initial condition y'(∏/8) = √2, which may influence the determination of C1 and C2, but this has not been fully explored in the discussion.
What is the dif. eq. you're trying to solve?cowmoo32 said:Homework Statement
y(x) = C1sin(2x) + C2cos(2x)
Homework Equations
y(∏/8) = 0
The Attempt at a Solution
C1(1/2)(√2) + C2(1/2)(√2) + 1 = 0
The book jumps to the equation below and I'm having trouble figuring out how they got there.
C1 + C2 = -√2
That doesn't make sense, unless you are asking if you can replace C1/2 by C1 and C2/2 by C2 .cowmoo32 said:I guess it's safe to assume that C1/2 = C1 and C2/2 = C2 considering they're both unknowns at this point?