How do I fix my graph?

The original ODE is: $($y$-1)^2($dy$/$dx$)=2$x$+3$

$[115]$: fig $=$ plt$.$figure$()$ # Creates a new figure

x $=$ np$.$arange$(1,11/3-0\mathrm{.}01,0\mathrm{.}1)$ # Defines the domainf$1=1-(((-81$x$2)/2-(243$x$)/2+(((-81$x$**2-243$x$+27)**2)1/2)/2+27/2)(1/3))/3$

plt$.$plot$($x$,$ f$1,$ color$=$'red'$)$def $\}$vf$($x$,$t$)$

dx $=$ np$.$zeros$(2)$

dx$[0]=1$

return dxX$,$ Y $=$ np$.$meshgrid$($np$.$linspace$(1,5,20),$ np$.$linspace$(0\mathrm{.}2,0\mathrm{.}6,20))$ # Sets $2-$dim domain

U$\}=1.$

$\backslash$mathrm $\{$ V $\}\backslash$mathrm $\{=\}\backslash$mathrm $\{(2*$X$+3)/(($Y$-1)**2)\}\backslash$mathrm $\{$ # ODE $\}\backslash$mathrm $\{$ right $\}\backslash$mathrm $\{$ side $\}\backslash$mathrm $\{$ also $\}\backslash$mathrm $\{$ goes $\}\backslash$mathrm $\{$ here $\}\backslash$mathrm $\{$ with $\}$ X for x and Y for yN $=$ np$.$sqrt$($U$**2+$ V$***2)$ # Don't modify

U $=$ U $/$ N # Don't modify

V $=$ V $/$ N # Don't modify

plt$.$quiver$($X$,$ Y$,$ U$,$ V$,$ angles$="$xy$")$

$[115]$: