Form the differential equation from the following primitives wher… - Vidyadip

Question

Form the differential equation from the following primitives where constants are arbitrart:

$\text{y}=\text{ax}^2+\text{bx}+\text{c}$

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Answer

The equation of family of curves is
$\text{y}=\text{ax}^2+\text{bx}+\text{c}\ ...(1)$
where a, b and c is an arbitrary constant. so, we shall get a differential equation of third order.
Differentiating equation (1) with respect to x, we get
$\frac{\text{dy}}{\text{dx}}=2\text{ax}+\text{b}\ ...(2)$
Differentiating equation (2) with respect to x, we get
$\frac{\text{d}^2\text{y}}{\text{dx}}=2\text{a}\ ...(3)$
Differentiating equation (3) with respect to x, we get
$\frac{\text{d}^3\text{y}}{\text{dx}3}=0$
It is the required differential equation.

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