Question

form the differential equation for y^2= (x+c) ^3

Answer 1

Step-by-step explanation:

c(y+c)

2

=x

3

....(i)

Differentiating both sides w.r.t x

2c(y+c)y

′

=3x

2

......(ii)

(i)

(ii)

⇒

y+c

2y

′

=

x

3

⇒c=

3

2

y

′

x−y

Now using (ii)

⇒2y

′

.(

3

2

y

′

x−y).

3

2

y

′

x=3x

2

⇒4(y

′

)

2

(2y

′

x−3y)=27x

⇒12y(y

′

)

2

=x[8(y

′

)

3

−27]

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