Using Laplace transform technique, solve the following initial value p

Question

Using Laplace transform technique, solve the following initial value problem:

$\frac{dx}{dt}+\frac{dy}{dt}=t,\frac{d^2x}{dt^2}-y=e^{-t},$

$x(0)=0,y(0)=0,\frac{dx}{dt}=0,$ for $t=0.$

22 Mar 2023

Answer :

Word Count : 249

To solve the given initial value problem using Laplace transforms, we first take the Laplace transform of each equation with respect to t, using the initial value conditions:

$sX(s) + sY(s) = \frac{1}{s^2}$
$s^2 X(s) - s x(0) - \frac{dx}{dt}(0) - Y(s) = \frac{1}{s+1}$

We can simplify the second equation using the initial value condition _______ ______ __________ _______ ___ _________ _____ _______ _______.
_____ ________ ___ ______ ____ _______.
_________ ___ ____ ________ ___ ___ ______ ____ ________ _______ ______ _____.
_________ ________ _______ __________ _____ __________ ___ _______ __________ __________ ________.
_____ ____ _____ ____ _____ ______ ________ _____ ____.
____ __________ _____ _____ __________ ____ ____ __________.
____ ________ ___ _____ _____ ________ __________ ___.
________ ____ ______ ________ ___ _______ ________ ________.
___ ___ ____ _____ ________ __________ _____.
_________ ____ ________ ____ __________ ___ _____ __________ ______ ___.
_________ ______ ______ ______ _______ ___ _____ ____.
_______ __________ _____ _________ _______ _____ __________.
___ ________ ____ _____ ____ _________ _______ ______ ___ ____ _________.
___ _________ ___ ________ ________ ___ ___ ________ _____ __________.
_______ ___ __________ _______ ____ _________ __________ __________ ______ ___ _____ ________.
_____ ______ __________ ______ ___ __________ ___ ________.
________ ________ _____ __________ ______ _____ ______ _________.
________ _____ _____ _________ _________ ____ _____ _____ __________ _______ __________.
________ _____ _______ ____ __________ ______ ______.
___ ________ ___ ______ _____ ____ __________ _______ ______ ________.
_______ ______ ___ _________ ________ ___ _______.
Get Full Answer on WhatsApp