Consider the following differential equation and initial value.

y$=2$x $3$y $+1,$ y$(1)=4$;$$ y$(1\mathrm{.}2)$

Use Euler's method to obtain a four$-$decimal approximation of the indicated value. Carry out the recursion of the equation

yn $+1=$ yn $+$ hf$($xn$,$ yn$).$

First, use increment

h $=0\mathrm{.}1.$

y$(1)=4$

y

$$y$(1\mathrm{.}2)$

Then, use increment

h $=0\mathrm{.}05.$

$($Round your answers to four decimal places.$)$

y$(1)=4$

y

$$y$(1\mathrm{.}1)$

y

$$y$(1\mathrm{.}2)$