2015 SQA Advanced Higher Mathematics No.16 Second order differential equation

Find the particular solution to a second order differential equation given initial conditions. Instructional exercise consisting of question 16 from the 2015 SQA Advanced Higher Mathematics examination. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the worked solution to each part of the question. Including indications of where each mark is allocated, and the requirements for that mark, according to the marking scheme.