Second-order differential equation and conditions

[Taylor_1989]

Homework Statement

Hy guys I am have a problem with the last part of this question. part d), ii) I get the general formal which I have displayed below, but what I done understand is if I take the limits as show in ii) I get $0=\ \infty$ which obviously I am doing something wrong. Have I misinterpreted what they are say as y tends to 0 as x tends. Could anyone give me some advice it would be much appreciated, thanks in advance.

Homework Equations

The Attempt at a Solution

$y=c_1e^{2x}+c_2e^{-3x}-e^{-x}$

 

[Mark44]

Homework Statement

Hy guys I am have a problem with the last part of this question. part d), ii) I get the general formal which I have displayed below, but what I done understand is if I take the limits as show in ii) I get $0=\ \infty$ which obviously I am doing something wrong. Have I misinterpreted what they are say as y tends to 0 as x tends. Could anyone give me some advice it would be much appreciated, thanks in advance.
View attachment 115277

Homework Equations

The Attempt at a Solution

$y=c_1e^{2x}+c_2e^{-3x}-e^{-x}$

What equation did you get for question d) part i)? Part ii) is essentially saying that $\lim_{x \to \infty} c_1e^{2x} + c_2e^{-3x} - e^{-x} = 0$. What are the values of the two constants so that this can happen?

 

[Taylor_1989]

@Mark44 I see now thank you as soo as u put in that form and do each lim seperatly I saw what was going on. Much apprectied.