Question

Cho \(y=x.e^{-\frac{x^2}{2}}\). Chứng minh hệ thức \(xy'=\left(1-x^2\right)y\)

Answer 1

Ta có : \(y'=e^{-\frac{x^2}{2}}+x\left(-x\right)e^{-\frac{x^2}{2}}=e^{-\frac{x^2}{2}}\left(1-x^2\right)\)

           \(xy'=\left(1-x^2\right)xe^{-\frac{x^2}{2}}=\left(1-x^2\right)y\)