To solve this equation, multiply by `y` and integrate:

`yy' = -9/16 x,` `int yy' dx = int (-9/16 x) dx,`

`y^2/2 = -9/32 x^2 + C,` or `y = +-sqrt(C - 9/16 x^2),`

where `C` is an arbitrary constant.

We need to find a suitable constant `C` using the...

## See

This Answer NowStart your **48-hour free trial** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

To solve this equation, multiply by `y` and integrate:

`yy' = -9/16 x,` `int yy' dx = int (-9/16 x) dx,`

`y^2/2 = -9/32 x^2 + C,` or `y = +-sqrt(C - 9/16 x^2),`

where `C` is an arbitrary constant.

We need to find a suitable constant `C` using the given point. The condition is `y(1) = 1,` or

`1 = +-sqrt(C - 9/16)` (+ is before the radical obviously).

This gives us `1 = C - 9/16,` so `C = 25/16` and the final answer is

`y(x) = +-sqrt(25/16 - 9/16 x^2).`