Show that y=ax^3+bx^2+c is a solution of the differential equatio… - Vidyadip

Question

Show that $\text{y}=\text{ax}^3+\text{bx}^2+\text{c}$ is a solution of the differential equation $\frac{\text{d}^3\text{y}}{\text{dx}^3}=6\text{a}$

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Answer

We have,

$\text{y}=\text{ax}^3+\text{bx}^2+\text{c}\ ...(1)$

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

$\frac{\text{dy}}{\text{dx}}=3\text{ax}^2+2\text{bx}\ ...(2)$

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

$\frac{\text{d}^2\text{y}}{\text{dx}^2}=6\text{ax}+2\text{b}\ ...(3)$

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

$\frac{\text{d}^2\text{y}}{\text{dx}^2}=6\text{a}$

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

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