# How to solve this questions using Differential Equation?

#### engineerahmedali004@gmail

Joined Jun 12, 2023
1

#### WBahn

Joined Mar 31, 2012
29,510
Are you expressly expected to use differential equations to solve these problems?

Here's how to solve it using differential equations:

Step 1: Set up the differential equations that describe the circuit behavior.

Step 2: Solve the differential equations.

Step 3: Impose the boundary conditions.

Depending on the technique you use to do this, the boundary conditions might be built into the solution implicitly or you might have to apply them explicitly.

Your currents in the first problem are not mesh currents, but rather loop currents. This makes using the standard approach more difficult, but not impossible. You just have to be even more careful to keep the bookkeeping straight.

So the next thing you need to do is show your best attempt to work the problems as far as you can and we can help you see where you might be going astray and get you back on track.

Please don't work both problems in the same thread -- we strongly encourage one problem per thread because otherwise you starting getting discussions of the two problems intermingled and chaos usually ensues. So pick one and let's focus on it.

#### RoofSheep

Joined Mar 7, 2023
36
Did you read the relevant chapter of the textbook these problems are from?

#### Exjay

Joined Nov 19, 2015
149
Solve the circuit with mesh analysis to obtain two equations for I1 and I2. Then, solve the differential equation using initial values. That is, at t=0 I1 and I2 are both zero.

#### MrAl

Joined Jun 17, 2014
10,906
Hello,

I always like to ask what have you done in the past like this. This will help guide what approach would be best for you here.

#### WBahn

Joined Mar 31, 2012
29,510
Hello,

I always like to ask what have you done in the past like this. This will help guide what approach would be best for you here.
It is increasingly looking like what they have done in the past is post their homework to websites expecting someone to do their work for them and blowing off any attempt to actually help them understand how to do it for themself.

#### Track99

Joined Jun 30, 2022
57
Write the loop equations in the form: Ri+L(di/dt)=V
You will have 2 loop equations cause you have 2 'windows'.
Solve for di/dt just like you would solve any algebraic equation for some unknown term.
You will integrate di/dt so that you will be able to figure out what the first i(t) is.
Plug the value of the first i(t) into any of the 2 loop equations and find out the second i(t).