Solving a differential equation: R/L I + dI/dt = V/L

[ehrenfest]

Can someone link me to a website that shows how to solve the DE

dI/dt + (R/L)I = V/L

where R is resistance, L is capacitance, I is current, V is voltage.

I understand how the solution works when you plug it in but I want to know the DE method that was used to get that solution.

 

[olgranpappy]

Can someone link me to a website that shows how to solve the DE

dI/dt + (R/L)I = V/L

where R is resistance, L is capacitance, I is current, V is voltage.

I understand how the solution works when you plug it in but I want to know the DE method that was used to get that solution.

Supposing that R and L (and why not V too) are independent of time, then just
multiply both sides by $$e^{t(R/L)}$$ and you can rewrite the LHS as
$$\frac{d}{dt}\left(Ie^{t(R/L)}\right)$$

and then integrate over time; the integral of the LHS is trivial and the integral of the RHS is just an exponential, then don't forget the constant term, etc and solve for I(t) with algebra.

 

[ehrenfest]

Thanks. I remember that from diffy q class now. What is that method called so I do not forget it again?

 

[Mindscrape]

Just use the general solution method. Find the homogeneous solution and the particular solution.

Olgran used an integrating factor.

 

[learningphysics]

Here's another method:
http://www.intmath.com/Differential-equations/Ans_5.php?a=0

separation of variables.