Basic Analysis I — Real Analysis · Problem 6.3.9

Sequences of Functions — Jiri Lebl

Mathematics — Real Analysis · picard-theorem-ode-uniqueness

Problem

Consider the equation

x y' = 2y

. (a)) Show that

y = Cx^2

is a solution for every constant

C

. (b)) Show that for every

x_0 \neq 0

and every

y_0

, Picard's theorem applies for the initial condition

y(x_0) = y_0

. (c)) Show that

y(0) = y_0

is solvable if and only if

y_0 = 0