Laplace transform for RC circuit capacitor voltage

[etotheix]

Homework Statement

Homework Equations

For a capacitor: i=C(de/dt)

The Attempt at a Solution

Using Kirchhoff's current law at the note above the resistor R2 I get the following equation, which I believe is right:

C(e0' - ei') + (e0 - ei)/R1 + e0/R2 = 0

Then, since the source has a constant voltage of A, I set ei' = 0 and ei = A and use Laplace to find the eo(t)

e0' + e0( 1/(C*R1) + 1/(C*R2) ) = A/(C*R1)

to facilitate the algebra:

1/(C*R1) + 1/(C*R2) = ( R1 + R2 )/( C*R1*R2 ) = ε1
A/( C*R1 ) = ε2

Then,

sE0 - E0(0) + (ε1)E0 = (ε2)/s

=> E0(0) = 0

E0( s + (ε1) ) = (ε2)/s

using partial fractions:

E0 = (ε2)/( s( s + (ε1) ) ) = A/s + B/( s+(ε1) )

A = ε2/ε1 and B = -ε2/ε1

ε2/ε1 = ( A*R2 )/( R1 + R2 )

E0 = (ε2/ε1)/s - (ε2/ε1)/( s + ε1 )

e0 = (ε2/ε1) - (ε2/ε1)e^(-ε1*t)

e0 = ( A )/( R1 + R2 )*( R2 - R2*ε1*t )

But I know that the answer to this problem is:

e0 = ( A )/( R1 + R2 )*( R2 - R1*ε1*t )

What am I doing wrong? Thanks in advance for any help!

 

[algebrat]

If you want to post in the math section, you should replace variables with x,y,z et cetera, and constants with a,b,c et cetera

 

[etotheix]

Sorry I am just trying to be consistent with the problem statement. Maybe I posted in the wrong forum (although my question is related to Laplace and not the circuit itself), maybe a moderator can move this to Homework & Coursework Questions > Engineering, Comp Sci, & Technology ?

Thanks.