Question

dy/dx = x/y , y(0) = −3

my answer: -(x^2+9)^1/2 , but this is wrong.

Answer 1

y dy = x dx
y^2/2 = x^2/2 + c
or
y^2 = x^2 + c

(-3)^2 = 0 + c
so
c = 9

y^2 = x^2 + 9

y = +/- (x^2+9)^(1/2)
since only y = -3 is given I think your answer correct