Question

Determine (without solving the problem) an interval in which the solution of the given initial value problem is certain to exist. (enter your answer using interval notation.) t(t − 9)y' + y = 0, y(1) = 1

Answer 1

If either
`t=0` or
`t=9`, the ODE has the trivial solution
`y=0`, but
`y(1)=1\\eq0`. So any solution to the ODE that satisfies the initial condition can only exist on the interval
`0<t<9`.