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Question
Form the differential equation from the following primitive where constants are arbitrary:
y = ax2 + bx + c
Solution
The equation of family of curves is \[y = a x^2 + bx + c\] ...(1)
where \[a, b\text{ and }c\] are arbitrary constants. So, we shall get a differential equation of third order.
Differentiating equation (1) with respect to x, we get
\[\frac{dy}{dx} = 2ax + b\] ...(2)
Differentiating equation (2) with respect to x, we get
Differentiating equation (3) with respect to x, we get
It is the required differential equation.
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