Solve the IVP,

$y^{\text{'}}=2+2(y-2x+9{)}^{\frac{1}{2}},$ with $y(0)=0.$

by using an appropriate substitution.

For $x_1=9,$ find $y(x_1).$

Include at least $3$ decimal places in each step in your calculation. Use $=3\mathrm{.}14159$ and $e=2\mathrm{.}71828.$