1. Let a and b be coefficients such that
Combining the fractions on the right gives
so that
2. a. The given ODE is separable as
Using the result of part (1), integrating both sides gives
Given that y = 1 when x = 1, we find
so the particular solution to the ODE is
We can solve this explicitly for y :
2. b. When x = 9, we get