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helpfulAnswer:
y^-2 = 2/x + 5/12Step-by-step explanation:
5. dy/dx = y³/x²
Seperate similar variables
dy/y³ = dx/x²
Integrating both sides
y^(-3+1) /(-3+1) = x^(-2+1) /(-2+1) + C
y^-2 / -2 = -1/x + C
Now, given that y(3) =2
Putting x=3 and y = 2
-1/8 = -1/3 + C
C = 1/3 -1/8 = 5/24
Therefore solution is
y^-2 / -2 = -1/x + 5/24
y^-2 = 2/x + 5/12
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