Differential Equations — Maths STD 12 Science — Question

(c) : We have given equation of parabola whose axes are parallel to $y$-axis.
$\therefore \quad$ Vertex is $(h, k)$
So, $(x-h)^2=4 a(y-k)$
On differentiating both sides, we get
$
2(x-h)=4 a \frac{d y}{d x}
$
Again on differentiating both sides, we get
$
2=4 a \frac{d^2 y}{d x^2}
$
Again, on differentiating both sides, we get $0=4 a \cdot \frac{d^3 y}{d x^3}$
$
\begin{aligned}
& \Rightarrow \frac{d^3 y}{d x^3}=0 \\
& \Rightarrow y_3=0
\end{aligned}
$