Use-Laplace-transform-to-solve-the-differential-equation-d-2-v-t-dt-2-6-dv-t-dt-8v-t-2u-t-when-v-0-1-and-v-0-2- Tinku Tara June 4, 2023 Differential Equation 0 Comments FacebookTweetPin Question Number 184936 by MikeH last updated on 14/Jan/23 UseLaplacetransformtosolvethedifferentialequationd2v(t)dt2+6dv(t)dt+8v(t)=2u(t)whenv(0)=1andvβ(0)=β2 Answered by hmr last updated on 15/Jan/23 L{vβ³}+6L{vβ²}+8L{v}=2L{u}β(s2L{v}βsv(0)βvβ²(0))+6(sL{v}βv(0))+8L{v}=2L{u}β(s2+6s+8)L{v}βs+2β6=2L{u}β(s2+6s+8)L{v}=2L{u}+s+4βL{v}=2L{u}+s+4s2+6s+8βL{v}=2L{u}+(s+4)(s+4)(s+2)βL{v}=2L{u}(s+4)(s+2)+1s+2βL{v}=2L{u}(s+4)(s+2)+L{eβ2t}βL{v}=4L{u}s+4β2L{u}s+2+L{eβ2t}βL{v}=4L{eβ4t}L{u}β2L{eβ2t}L{u}+L{eβ2t}Sorrythatβ²sallIknow. Commented by MikeH last updated on 15/Jan/23 thanksalot Commented by hmr last updated on 15/Jan/23 Youβ²reWelcome Commented by hmr last updated on 15/Jan/23 Ieditedthelastline,Itwaswrong! Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: If-f-2-R-f-x-x-2-1-1-x-2-f-1-pi-Next Next post: Question-53867 Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.