5. Consider the differential equation
xy^5/2 +1+x^2y^3/2dy/dx =0
(a) Show that this differential equation is not exact.
(b) Find a value for the constant a such that, when you multiplythe d.e. through by xa, it becomes exact. Show your working. Do NOTsolve the resulting differential equation.
6. Consider the differential equation
(D − 3)(D − 4)y = 0.
(a) Solve this d.e., showing brief working.
(b) How many solutions does this d.e. have? Justify youranswer.
(c) How many independent solutions does this d.e. have? Providea calculation to justify your answer.
