The discussion revolves around eliminating constants from a differential equation involving the functions y, y', and y''. The original poster presents the equations and expresses uncertainty about how to proceed with the elimination of constants c1 and c2.
Some participants have offered guidance on how to approach the problem, suggesting specific substitutions and manipulations. There is an acknowledgment of progress made by the original poster in deriving an expression for c2, although there remains some confusion regarding the correct form of the expression.
Participants are working within the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is an ongoing discussion about the accuracy of derived expressions and the implications of different forms of the equations.
What do you get if you plug y = (c1 +c2x)ex for the second term in y' ?th3chemist said:Homework Statement
eliminating c1 and c2 from y, y' and y'' to create a differential equation
Homework Equations
I have the equation y = (c1 +c2x)e^x
y' = c2e^x +(c1+c2x)e^x
y'' = c2e^x + c2e^x + (c1+c2x)e^x)
(from product rule)
The Attempt at a Solution
I'm just not sure how to eliminate the constants. If I try to do y'' - y i still have constants left.
SammyS said:What do you get if you plug y = (c1 +c2x)ex for the second term in y' ?
Solve that for c2.
th3chemist said:thank you! I can't believe I didn't see that.
I got c2 = (y' - y) e^x. I can then sub this into y'' to get the differential.
Thank you :)
lendav_rott said:Isn't it c2 = (y' - y) e^-x ?