(a) show that all the solutions of the linear equation u+a(t}u = 0,t e [0, co), where a: [0, co) [0,co) is a continuous function, are always bounded if jo a(s)d

(a) Show that all the solutions of the linear equation u+a(t}u = 0,t E [0, co), where a: [0, co) [0,co) is a continuous function, are always bounded if Jo a(s)ds< 0o. (b) Consider the equation (1+tu-u = 0, te [0, o). (i) Find the unique solution. i) Show that lu(0) connecting this result with the problem (2) (a)? lu(t)| < lu{0)]e, for all t E [0,0o). How you are