Get personalized answers to your specific questions with IDNLearn.com. Get the information you need from our community of experts who provide accurate and thorough answers to all your questions.
Sagot :
The Laplace of the given equation is [tex]y=-\frac{15e^2}{8}e^{2t}+\left(-3e^2+\frac{15e^2}{4}\right)e^{2t}t+\frac{e^2t^4}{4}+e^2t^3+\frac{9e^2t^2}{4}+3e^2t+\frac{15e^2}{8}[/tex].
According to the statement
we have given that the equation and we have to solve this problem with the help of the Laplace transform.
So, According to the statement
the given equation is
y'' − 4y' + 4y = t^3e^2t, y(0) = 0, y'(0) = 0
And the Laplace transform is an integral transform method which is particularly useful in solving linear ordinary differential equations.
Firstly fill the value of the Laplace of the second order derivative and put x = 0 in the equation
And same it with the first order of the derivative.
And then the Laplace of the equation become
[tex]y=-\frac{15e^2}{8}e^{2t}+\left(-3e^2+\frac{15e^2}{4}\right)e^{2t}t+\frac{e^2t^4}{4}+e^2t^3+\frac{9e^2t^2}{4}+3e^2t+\frac{15e^2}{8}[/tex]
So, The Laplace of the given equation is [tex]y=-\frac{15e^2}{8}e^{2t}+\left(-3e^2+\frac{15e^2}{4}\right)e^{2t}t+\frac{e^2t^4}{4}+e^2t^3+\frac{9e^2t^2}{4}+3e^2t+\frac{15e^2}{8}[/tex]
Learn more about Laplace transform here
https://brainly.com/question/17062586
#SPJ4
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Your questions are important to us at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.
