Form the differential equation of the family of curves represented `c(y+c)^2=x^3, w h e r e` is a parameter.

Explanation

`c(y+c)^{2}=x^{3} ldots . .(1)`


Differentiating both sides w.r.t x
`

2 {c}(y+c) {y}^{prime}=3 {x}^{2} ldots ldots { (ii) }`
`

Rightarrow frac{2 y^{prime}}{y+c}=frac{3}{x} Rightarrow c=frac{2}{3} y^{prime} x-y`

Now using (ii)
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