Yah I know that rule. I guess I just didn't figure a substitution needed to be done here as we've never really used one like you did in our problems. Why the +/- though? I suppose that's because it is still an intro to Differential Equations. And also I was wondering what your 3rd line was about, but I see now. And the "sloppy" method of treating the derivative as a fraction. That's the method I was taught in class so far

Edit:

$\displaystyle y=-e^{-\frac{x^2}{2}}e^{-C} + 1 \rightarrow 0=-e^{-\frac{(1)^2}{2}}e^{-C} + 1$

$\displaystyle -\frac{1}{e^{-C}}=-e^{-\frac{1}{2}} \rightarrow \color{red}{-e^C=-e^{\frac{1}{2}}}$

$\displaystyle \ln-e^C=\ln-e^{\frac{1}{2}} \rightarrow -C=-\frac{1}{2}$

$\displaystyle C=\frac{1}{2}$

So this is what you were getting at basically? If not where did I go wrong?

Plug back in:

$\displaystyle y=-e^{\frac{-x^2-1}{2}} + 1$