I got the answer y= cubic sqrt of everything in the brackets ((3/2x^2) + 8)
I'm not sure if it's right.
Thanks
What is the equation of the curve? The slope of the curve at a point (x,y) is of x/y^2 and the curves goes through (0,2).?
2016-08-01 6:35 am
回答 (1)
2016-08-01 6:44 am
✔ 最佳答案
Slope of the curve at a point (x, y) :dy/dx = x/y²
y² dy = x dx
y² dy = x dx
∫y² dy = ∫x dx
(1/3)y³ = (1/2)x² + C₁
2y³ = 3x² + C
The curve goes through (0, 2). Then, when x = 0, y = 2 :
2(2)³ = 3(0)² + C
C = 16
Equation of the curve :
2y³ = 3x² + 16
3x² - 2y³ + 16 = 0
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