Find the largest interval which includes x = 0 for which the given initial-value problem has a unique solution. (Enter your answer using interval notation.) (x − 3)y'' + 4y = x, y(0) = 0, y'(0) = 1

Step-by-step explanation:

We are given that

y(0)=0

y'(0)=1

By comparing with

We get

q(x)=0

p(x),q(x) and g(x) are continuous for all real values of x except 3.

Interval on which p(x),q(x) and g(x) are continuous

and (3,

By unique existence theorem

Largest interval which contains 0=

Hence, the larges interval on which includes x=0 for which given initial value problem has unique solution=

the answer is b