For the ones that would like to try MATLAB: Let$$s use MATLAB

to plot the vector field corresponding to the right$-$hand side of ODE

dy

dx $=2$x$.(1)$

Execute the following commands in the MATLAB command window:

$1.$ Create a mesh in the $($x$,$ y$)-$plane:

$[$x$,$y$]=$meshgrid$(-5$:$0\mathrm{.}2$:$5)$;

$2.$ For each point of the mesh, calculate x and y coordinates of vector tip:

dx$=1$;

dy$=2*$x;

$3.$ Calculate the vector length:

r$=($dx$.^2+$dy$.^2).^0\mathrm{.}5$;

$4.$ Divide coordinates with vector length to normalize the vector:

px$=$dx$./$r;

py$=$dy$./$r