write the pythons please

Consider the differential equation

$\frac{dy}{dx}=x^{2}y$

Use the ideas from the previous exercises to determine which of the following functions are solutions to the differential equation:

$y_1(x)=e^x,y_2(x)=e^{\frac{x^2}{2}},y_3(x)=e^{\frac{x^3}{3}}$

$2]$:

$\frac{?}{?}$# Define right$-$hand side

def $f(x,y)=$ return

A Define the three functi

$y^1=sp*exp(x)$

$y^2=sp*exp(\frac{x^{****2}}{2})$

$y^3=sp*exp(\frac{x^{****3}}{3})$

ND Define the three functions $y^2,y2,y3$

First, use the approach in Exercise $1$ to have Python verify whether each function is a solution to the differential equation.

# Check whether $y_{-}1$ is a solution

# Check whethor $y_{-}2$ is a solution