🔵25 - D Operator Method for Solving Second Order Linear Differential Equations

In this lesson we shall learn how to solve the general solution of a linear differential equation using the d operator method. The d operator is an effective way of solving d.e's where the coefficients need to be constants.
For each form of G(x), the solution process is quite different.

In this lesson we shall consider variety of cases and examples i.e
for g(x) to be a:
1. Exponential Function
2. Sine or cosine function
3. Polynomial function
4. sum of functions
5. product of functions

00:00 - Ex 1: Exponential Function
03:53 - Ex 2: Polynomial function
08:45 - Ex 3: sine or cosine function
12:43 - Ex 4: product of functions

Playlists on various Course
1. Applied Electricity

2. Linear Algebra / Math 151

3. Basic Mechanics

4. Calculus with Analysis / Calculus 1 / Math 152

5. Differential Equations / Math 251

6. Electric Circuit Theory / Circuit Design

Make sure to watch till the end.
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Thank you.

[HardFlip]

Just learned this from my Proff, super helpful

[ahmedalosais]

16:46 why not let D^{2} = -a^{2} = -1 > which eventually gives -cosx instead of integrating twice

[Dummy-]

What if on the RHS we have (x^2+3x+1)e^2x or (x^2+3x+1)cos3x then what will we do??

[vuyiswampanza]

Thank you sir for making such understandable videos keep it up

[sechabatheletsane]

Can you please derive the formulas so that we gain deeper understanding

[bigsam]

what if the a value for tge exponential and trigonometric functions are different

[ojehagbaje]

Very helpful but the part I don't understand is in the 3rd example, why is -2²=-4 and not 4?

[umeshtanunautiyal]

Pls sir explain with a new bideo a=-1and D+a=D-a

[oganija]

Why do you keep using this method
Why not follow the formula approach

[kaursingh]

sir thank u -please name book thank u sir