# b.2.4.2 interval of initial value problem

#### karush

##### Well-known member
Determine an interval in which the solution of the given initial value problem is certain to exist

$t(t-4)y'+y=0 \quad y(2)=2\quad 0<t<4$

ok my first step was isolate y'
s
$y'=-\dfrac{y}{t(t-4)}$

not sure what direction to go since we are concerned about an interval

#### Country Boy

##### Well-known member
MHB Math Helper
Well, the problem specifically says "0< t< 4" and y' does not exist at t= 0 and t= 4.

#### karush

##### Well-known member
how does y(2)=2 fit into this
doesn't that give us specific y interval

#### topsquark

##### Well-known member
MHB Math Helper
how does y(2)=2 fit into this
doesn't that give us specific y interval
You could always do "brute force" if you can't figure out a work around. Boundary conditions get rid of integration constants. Solve the differential equation. What is y(t)? What does that tell you about the solution interval(s)?

-Dan