cant get to the same expression as the solution..

**broken link removed**
i tried to solve it by myself but
in my expression as you see i get a totally different expression when i do coefficient of exponent then the one in the solution
did i do it correctly
[latex][CR_1+C\alpha \beta R_2]\frac{-\beta }{\tau }e^\frac{-t }{\tau }+Be^\frac{-t }{\tau }=V_0e^\frac{-t }{\tau }[/latex]

the alpha and beta dissapeared
why?

Hi there,


A quick glance makes it look like they are simply lumping R1+alpha*beta*R2 into R as:
R=R1+a*b*R2

where a=alpha and b=beta and they are both constants.

If this is the case then you would get the same answer as they did.

Lookup linear first order differential equations
There is a topic that uses the integrating factor to solve this type of equations
Ex
Eq1
Eq2
We use an integrating factor
We multiply eq2 by the integrating factor
Eq3
We notice that the left hand side of equation 3 is the derivative of a product, namely (Calculus 1)
We make the substitution in eq3
Integrate both sides
Initial condition not applied
I also ran the Differential equation (DE) in Maple and the answer is correct. You also have to consider that this is not the only solution to the DE. ( review ODE)
hope it helped.
Can Math be written on this forum?