find an equation of the curve that passes through the point (1,1) and whose slope at (x,y) is y^2/x^3

Answer 1

dy/dx=y^2/x^3

y^-2 dy= x^-3 dx

-y^-1=-x^-2*1/2 + C

check:take the derivative.
y^-2 y'=x^-3
dy/dx=y^2/x^3

so find c at by putting 1,1 into the equation

1/y=1/x^2 + C