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## Homework Statement

evaluate dy/dx + y

^{2}+ 1 = 0

## The Attempt at a Solution

dy/dx + y

^{2}= -1

integtating factor I:- e

^{x + c}= e

^{x}e

^{c}= Ce

^{x}

so xboth sides by I and rearranging forms:- d/dx(e

^{x}y

^{2}) = -e

^{x}

integrating both sides:- e

^{x}y

^{2}= -e

^{x}+ c

so y

^{2}= -1 + Ce

^{-x}

y = SQRT[Ce

^{-x}-1]