QUESTIONS:
1)In each of the following, decide if the Existence and Uniqueness Theorem is applicable. Find, if exists, the solution(s) for each of items.
(a) y0 = 5y4/5, y(0) = 0.
(b) y0 = 5y4/5, y(0) = 1.
2) (a) Find the continuous solution to the initial value problem dy1 if |x| ≤ 1
+ y = q(x) where q( ) = satisfying y(0) = 0.
dx0 if |x| > 1
(b) Solve the differential equation
3) Let (3xy − y2)dx + x(x − y)dy = 0 be given.
(a) Show that the given equation is not exact.
(a) Find an integrating factor which makes the given equation exact and solve it as an exact differential equation.
