Consider a non$-$homogeneous $1$st order linear ODE:

$x{y}^{\text{'}}+y=1\mathrm{.}3e^x$

The general solution has structure $y=C{y}_c+y_p$ where

$y_c($Complementary solution$)$ is a solution to the associated homogeneous Equation: $x{y}^{\text{'}}+y=0$ with an arbitrary constant $C.$

$y_p$ is ANY particular solution to $x{y}^{\text{'}}+y=\text{'}$a $e^x..$

For $x_1=1\mathrm{.}2,$ find $\frac{y_p(z_1)}{y_c(x_1)}$

Include at least $3$ decimal places in each step in your calculation.

Use $=3\mathrm{.}14159,$ and $e=2\mathrm{.}71828$