Find 𝑑^2𝑦 𝑑𝑥^2 when 𝑥 = 𝑡^3 + 3𝑡^2 and 𝑦 = 𝑡^4 -8t^2
You asked:
Given \( x = {t}^{3} + 3 \cdot {t}^{2} \), \( y = {t}^{4} - 8 \cdot {t}^{2} \), evaluate \( {d}^{2} \cdot y \), \( d \cdot {x}^{2} \).
MathBot Answer:
The system of equations has infinitely many solutions.
$$\begin{aligned}d^{2} y&=d^{2} \left(t^{4} - 8 t^{2}\right)\\x^{2} d&=d \left(t^{3} + 3 t^{2}\right)^{2}\end{aligned}$$