$(1$ point$)$ Solve the initial value problem yy$^(\text{'})+$x$=\backslash$sqrt$($x$^(2)+$y$^(2))$ with y$(1)=\backslash$sqrt$(15).$

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

u$=($x$+$y$($du$)/($dx$))/($u$($du$)/($dx$))$ help $($formulas$)$

u$^(\text{'})=$ help $($formulas$)$ y$^(\text{'})$ for $($dy$)/($dx$)$ 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$)$