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in Differential Equations by (28.7k points)
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Form the differential equation from the following primitives where constants are arbitrary:

y = ax2 + bx + c

1 Answer

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Best answer

As the given equation has 3 different arbitrary constants so we can differentiate it thrice with respect to x

So, differentiating once with respect to x,

\(\frac{dy}{dx} = 2ax + b\)

Differentiating twice with respect to x,

\(\left(\frac{d^2y}{dx^2}\right)=2a\)

Now, differentiating thrice with respect to x we get,

\(\frac{d^3y}{dx^3}=0\)

Hence, \(\frac{d^3y}{dx^3}=0\) is the differential equation corresponding to y = ax2 + bx + c.

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