Question

Find the differential equation that will represent the family of curves given by (a, b: parameter):
y = ax³

Solution

The given equation is
y = ax^{3 ...(1)}

dy over dx space equals space 3 ax squared

...(2)
Dividing (1) by (2), we get

fraction numerator straight y over denominator begin display style dy over dx end style end fraction space equals straight x over 3

straight x dy over dx space equals space 3 straight y

which is required differential equation

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