(Solved): Solve for y(x) given that y+3y18y=36 subject to y(0)=9 and y(0)=21. (i) write dow ...

Solve for $$y(x)$$ given that $$y^{??}+3y^{?}?18y=36$$ subject to $$y(0)=9$$ and $$y^{?}(0)=?21$$. (i) write down and solve the associated auxillary equation (ii) hence determine the natural response function (complementary function). (iii) determine the forced response function (particular integral) (Iv) hence find an expression for $$y(x)$$ which satisfies both the differential equation and the given initial conditions. Note that although the question is in four parts, this is for your guidance only. For this question please just enter the form of the particular solution, as a function of $$x$$ in the following box: