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 ?
Eliminating constants helps to isolate and identify the effects of independent variables in an experiment. It allows for more accurate and reliable conclusions to be drawn.
Constants that are not relevant to the research question or hypothesis can be eliminated. It is important to carefully consider which variables are truly independent and which may be influenced by other factors.
No, eliminating constants does not in itself lead to biased results. However, it is important to carefully consider which constants are eliminated and to ensure that the remaining variables are truly independent.
In some experiments, constants may not need to be eliminated if they do not have a significant impact on the independent variable. However, it is always important to carefully consider the potential effects of all variables in an experiment.
Identifying which variables are truly independent and which may be influenced by other factors can be challenging. Additionally, eliminating constants may limit the generalizability of the results, as the experiment may not accurately reflect real-world conditions.