Session 10: Laplace Transforms to solve differential equations (Initial Value Problem)

In this video we will see how laplace transforms are used to solve initial value problem of a differential equations. Here specifically we will see differential equations with contant coefficients and intial conditions at x=0.
We will see the main theorem of laplace on Laplace of derivatives for first order, second order and upto nth order.

We will see the nice conditions which function needs to satisfy in order laplace of derivative to exist. We will also see some examples which will help us to understand the theorem and solve differential equations.
=======================================
Links for previous lectures:

===================
Existence Theorem of Laplace transforms

======================================
What are Laplace transforms:

=====================================
Examples on Laplace Transforms:

======================================
Exponential growth : Concept and Examples:

=====================================

[chaitanyapatil]

Sir at 10.56 won't the factors will be (s+3) and (s+4) ?

[charusheeladeshpande]

nice video. Just one comment - the third condition in Laplace Transform of derivative formula ensures that LHS exists and only then it can be equal to RHS. Ofcourse one should be able to prove that if f is of exponential order then so is its derivative!

[adeshchoudhar]

Sir, I'm getting the answer as, y = 3e^t + e^(-2t) - 2.

[rahulthorat]

Sir, it is necessary that y is function of 't'. If it is function of x then also this method is useful??
I mean it possible to replace x by t so we can solve

[motivationalworld]

sir pleae make more and more videos like this

[YasaswiniSankula]

I got stuck at solving Laplace inverse of (2s^2+3s+4)/s^2+s-2

[rahulthorat]

Ans homework problem
y= (-1/3*e^(-2t))+(1/3*e^(t))-2

[YasaswiniSankula]

sir can you please send the sol'n