SUCCESSIVE DIFFERENTIATION (Excercise)

\[\underline{PART\ -\ A}\]
\[1.\ Find\ the\ order\ and\ degree\ of\ the\ differential\ equation\ \frac{d^3y}{dx^3}\ -\ 5\ \frac{d^2y}{dx^2}\ +\ 6\ \frac{dy}{dx}\ +\ 7\ y\ =\ 0\ \hspace{10cm}\]
\[\color {black}{Solution:}\ order\ =\ 3,\ degree\ =\ 1\ \hspace{15cm}\]
\[\underline{PART\ -\ B}\]
\[2.\ Form\ the\ differential\ equation\ of\ y^2\ =\ 4\ a\ x\ by\ eliminating\ the\ constant\ ‘a’\ \hspace{15cm}\]
\[\color {black}{Solution:}\ y^2\ =\ 4\ a\ x\ \hspace{15cm}\]
\[Differentiate\ w.\ r.\ t.\ x\ on\ both\ sides\ \hspace{10cm}\]
\[\frac{d}{dx}( y^2)\ =\ 4\ a\ \frac{d}{dx}( x)\ \hspace{10cm}\]
\[2\ y\ \frac{d}{dx}(y)\ =\ 4\ a\ (1)\ \hspace{10cm}\]
\[2\ y\ \frac{dy}{dx}\ =\ 4\ a\ \hspace{10cm}\]
\[\frac{dy}{dx}\ =\ \frac{4\ a}{2\ y}\ \hspace{10cm}\]
\[\frac{dy}{dx}\ =\ \frac{2\ a}{y}\ \hspace{10cm}\]