Problem $1.$ Solve the following differential equation, Please show the code and plot the results and show all the plots.

$y^{\text{'}}=-x^{2}y,y(0)=1,$

by:

Exactly $($analytically$).$

Euler's method.

Runge$-$Kutta method.

and plot the three results in a single graph. Use $0x1$ and $h=0\mathrm{.}1.$

Use the following syntax:

plot "data$1.$txt$",$ "data$2.$txt$",sin(x)$

where "data$1.$txt$"$ contains data from the Euler method and "data$2.$txt$"$ contains data from the R$-$K method.