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

Question

Form the differential equation from the following primitives where constants are arbitrary: y = ax 2 + bx + c

Philoid · Accepted 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,

Differentiating twice with respect to x,

Now, differentiating thrice with respect to x we get,

Hence, is the differential equation corresponding to

y = ax² + bx + c.