Consider the following initial value problem: ð‘¦â€³ − 2ð‘¦â€² − 35𑦠= sin(5ð‘¡), ð‘¦(0) = 4, ð‘¦â€²(0) = −3. Using 𑌠for the Laplace transform of ð‘¦(ð‘¡), i.e., 𑌠= ð¿{ð‘¦(ð‘¡)}, find the equation you get by taking the Laplace transform of the differential equation and solve for ð‘Œ(ð‘ ).