Verified answer

x^2*y'-2*x*y=1

у=x^2*z

у`=x^2*z`+2x*z

x^2*y'-2*x*y=1

x^2*(x^2*z`+2x*z)-2*x*x^2*z=1
x^2*(x^2*z`)=1

dz = dx/x^4

z=-1/3x^3 + c

у=x^2*z = c*x^2 - 1/(3x)

y(1) = c-1/3=5

c = 16/3

ответ

y = 16*x^2 /3 - 1/(3x)