$(1$ point$)$ Solve the initial value problem

$y{y}^{\text{'}}+x=\sqrt[\phantom{2}]{x^2+y^2}$ with $y(5)=\sqrt[\phantom{2}]{56}$

a$.$ To solve this, we should use the substitution

$u=$ help $($formulas$)$

$u^{\text{'}}=$ help $($formulas$)$

Enter derivatives using prime notation $($e$.$g$.,$ you would enter $y^{\text{'}}$ for $\frac{dy}{dx}).$

b$.$ After the substitution from the previous part, we obtain the following linear differential equation in $x,u,u^{\text{'}}.$

help $($equations$)$

c$.$ The solution to the original initial value problem is described by the following equation in $x,y.$ help $($equations$)$