I have the following equation with β∈[0,1] and δ∈[0,1] are 2 parameters and $\mu$, $\sigma$ are the mean and standard deviation of a random variable. Is it possible to use software to get the explicit expression of the solution.
$\left[ \Phi\left( \dfrac{x-\mu}{\sigma}\right)-\delta\right] \phi\left( \dfrac{x-\mu}{\sigma}\right)+\left[ \dfrac{x-\mu}{\sigma}\right] f\left( \Phi\left( \dfrac{x-\mu}{\sigma}\right)\right) =0$
with $f(p)=\dfrac{p^{2}}{2}- \delta p+\left( \dfrac{\delta^{2}}{2} + \beta\right)$
Where $\Phi$ and $\phi$ are the cumulative distribution and the density function of Gaussian distribution. I want to solve this equation usin Maple or Mathematica, but I was not able to do it.