Question
Show that $\text{y}=\text{ax}^3+\text{bx}^2+\text{c}$ is a solution of the differential equation $\frac{\text{d}^3\text{y}}{\text{dx}^3}=6\text{a}$
✓
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.
$\text{y}=\text{ax}^3+\text{bx}^2+\text{c}\ ...(1)$
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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