Short Answer Type
The equation of curve is
...(1)
Differentiating w.r.t., x successively two times, we get.
or 
...(2)
...(3)
and 
...(4)
From (3), (4), we get,
which is the required differential equation.
Find the differential equation that will represent the family of curves given by (a, b: parameter):
y = ax3
Find the differential equation that will represent the family of curves given by (a, b: parameter):
x2 + y2 = a x3
Find the differential equation that will represent the family of curves given by (a, b: parameter):
y = eax
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