give the largest interval i over which the general solution is defined. explain !
(x^2-1)dy/dx+2y=(x+1)^2

Divide both sides by to get a linear ODE,

In order for this operation to be valid in the first place, we require that (since that would make undefined, which we don't want to happen). Then we are forcing any solution to the ODE to exist on any of the three intervals, , , or , and either the first or third of these can be chosen as the largest interval.

In case you also need to solve the ODE: Multiply both sides by , so that

Then the left side can be condensed as the derivative of a product, since

and we have

Integrate both sides:

step-by-step explanation :

we know that

the measurement of the outer angle is the semi-difference of the arcs which comprises

in this problem

m< xzy is the outer angle

substitute the values

the measure of angle xoy is equal to

> by central angle

substitute the value