ty' = y+√(t^2+y^2)
let y=vt
then y' = v + tv'
Now we have
t(v+tv') = tv+√(t^2+(tv)^2)
tv + t^2v' = tv + t√(1+v^2)
t^2v' = t√(1+v^2)
tv' = √(1+v^2)
dv/√(1+v^2) = dt/t
arcsinh(v) = lnt + c
v = sinh(c+lnt)
y= vt = t*sinh(c+lnt)
whew
solve initial value problem
t dy/dt = y + sqrt(t^2 + y^2) , y(1)=0
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