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 − 5)y'' + 3y = x, y(0) = 0, y'(0) = 1

The largest interval is    

Step-by-step explanation:

From the question the equation given is  

Now dividing the both sides of this equation by (x-5)

Comparing this equation with the standard form of 2nd degree differential which is

We see that

So at x =  5   are defined for this equation because from the equation of  x =  5 give infinity

This implies that the largest interval which includes x = 0 , P(x) , Q(x) , R(x ) is  

This because x = 5 is not defined in y domain

step-by-step explanation:

5x+10 is the correct one

hope this