Question

Show that y = ax³ + bx² + c is a solution of the differential equation \[\frac{d^3 y}{d x^3} = 6a\].

 

Answer 1

We have,

\[y = a x^3 + b x^2 + c ...........(1)\]

Differentiating both sides of (1) with respect to x, we get

\[\frac{dy}{dx} = 3a x^2 + 2bx ...........(2)\]

Differentiating both sides of (2) with respect to x, we get

\[\frac{d^2 y}{d x^2} = 6ax + 2b..............(3)\]

Differentiating both sides of (3) with respect to x, we get

\[\frac{d^3 y}{d x^3} = 6a\]

Hence, the given function is the solution to the given differential equation.