Hello everyone, this issue reads:

Find the orthogonal trajectories of the family of curves$\displaystyle y = C_1e^{-x} $

Well, by definition, the steps are these:

First solve for $\displaystyle C$. and $\displaystyle C = \displaystyle\frac{y}{e^ {-x}}$

differentiate the equation:

$\displaystyle

y * (y\prime) + Ce^{-x} = 0 $, you get rid of the constant C and finally going to be that, by definition,

$\displaystyle y_2' = - \displaystyle\frac{1}{y'}$

But I have problems to find the answer of the book is

$\displaystyle \displaystyle\frac{y^2}{2} = x + C$

Thank you very much,

greetings