Use the given differential equation for electrical circuits given by In this equation, I is the current, R is the resistance, L...

Given ,

=>

now dividing with L on both sides we get

=>

=>

which is a linear differential equation of first order

Solve the differential equation for the current given a constant voltage

so

So , Re-writing the equation (1) as,

(1) => -----(2)

On comparing the above equation with the...

Given ,

=>

now dividing with L on both sides we get

=>

=>

which is a linear differential equation of first order

Solve the differential equation for the current given a constant voltage

so

So , Re-writing the equation (1) as,

(1) => -----(2)

On comparing the above equation with the general linear differential equation we get as follows

---- (3)       -is the general linear differential equation form.

so on comparing the equations (2) and (3)

we get,

and

so , now

let us find the integrating factor

so now ,

=

=

So , now the general solution for linear differential equation is

=>

=> -----(4)

 Now let us evaluate the part

this is of the form

and so we know it is equal to

=

so , now ,

where

so ,

now substituting  in the   equation (4) we get ,

upon cancelling and   , we get

so ,

  is the solution