Anneliese and Trishanti would like to find the solution the following ordinary differential equation. (DE) 23 dy =y" +17x-y, x>0. da (a) Anneliese wishes to determine the type of this ordinary differential equation. Select all the true statements from those below. O (DE) is an exact ordinary differential equation O (DE) is a separable differential equation O (DE) is a linear ordinary differential equation O (DE) is a first order differential equation (b) Trishanti notices that there is a trivial solution yo (x) for (DE) of the form yo (a) = C for any x, where C' is some real constant. Enter down the value of C. C =(c) To find non-trivial solutions for (DE), Trishanti suggests Anneliese to use the substitution y = av(x) to convert the ordinary differential equation (DE) in a simpler differential equation. This becomes dv + 16v (DE2) dx Select all the true statements from those below. O (DE2) is a separable differential equation O (DE2) is an exact ordinary differential equation O (DE2) is a linear ordinary differential equation O (DE2) is a first order differential equation (d) Anneliese notices that a bu + c + 73 + 16v U2 + 16 for some constants a, b and c. Write down the values of a, b and c in the boxes below. a = b C =(e) Using (c), (d), Anneliese and Trishanti solve the differential equation (DE 2) and obtain a solution v = v(a) that satisfies In |v| + h(v) = 16 In |x| + D, for some function h and some constant D. Write the expression of h(v) (in terms of the variable v). h(v ) = Syntax advice: Enter your answers as exact expressions using Maple syntax. For example, use 4*log (6*v) or 2*log (abs (5*v) ) or 5*sec (9*Pi*v) or 7*tan (6/v) or 3*arctan (v/5) for 4 log(6v) or 2 log |5v| or 5 sec(9Tru) or 7 tan(6/v) or 3 arctan(v/5), respectively. Note that log is the natural logarithm. Then they conclude that y(a) = av(a) is a solution of the original differential equation (DE)