Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
If the initial value problem is [tex]y^{11} -8y^{1} -15y=0[/tex] and [tex]y^{1}(0) =1[/tex],y(0)=0 then y(t)=[tex](e^{3t} -e^{5t} )/2[/tex].
Given the initial value problem be [tex]y^{11} -8y^{1} -15y=0[/tex]and [tex]y^{1}(0) =1[/tex],y(0)=0.
We are required to find the solution of the given initial value problem.
Laplace transform is an integral transformation that converts a function of a real variable to a function of a complex variable.
Take laplace on the DE, we get
[tex]s^{2}-sY(0)-y^{i}(0)-8[sY(s)-y(0)-15Y(s)]=0[/tex]
[tex]s^{2}Y(s)-s(0)-1-8{sY(s)-0)}+15Y(s)=0[/tex]
(Putting the values given in question)
Y(s)=([tex]s^{2} -8s+15)-1=0[/tex]
Y(s)=1/([tex]s^{2} -8s+15[/tex])
Simplifying the above:
=1/([tex]s^{2} -5s-3s+15)[/tex]
=1/[s(s-5)-3(s-5)]
=1/2 [1/(s-3)-1/(s-5)]
Taking inverse of the above we get,
y(t)=[tex](e^{3t} -e^{5t} )/2[/tex]
Hence if the initial value problem is [tex]y^{11} -8y^{1} -15y=0[/tex] and [tex]y^{1}(0) =1[/tex],y(0)=0 then y(t)=[tex](e^{3t} -e^{5t} )/2[/tex].
Learn more about laplace transform at https://brainly.com/question/17062586
#SPJ1
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.