Dy/dx = y/(x^2) dy/y = dx/(x^2) int[dy/y] = int[dx/(x^2)] ... apply integral to both sides ln(|y|) = (-1/x) + C |y| = e^{(-1/x) + C} |y| = e^C*e^(-1/x) |y| = C*e^(-1/x) y = C*e^(-1/x)
So you have the correct answer. Nice job.
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Check: y = C*e^(-1/x) dy/dx = d/dx[C*e^(-1/x)] dy/dx = d/dx[-1/x]*C*e^(-1/x) dy/dx = (1/(x^2))*C*e^(-1/x) is the expression for the left hand side (LHS)
y/(x^2) = [C*e^(-1/x)]/(x^2) y/(x^2) = (1/(x^2))*C*e^(-1/x) is the expression for the right hand side (RHS)
Since LHS = RHS, this confirms the solution for dy/dx = y/(x^2)
