- Given that
$$y = 2 x ^ { \frac { 3 } { 2 } } - 1$$
- find \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }\),
- show that
$$4 x ^ { 2 } \frac { \mathrm {~d} ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } - 3 y = k$$
where \(k\) is an integer to be found,
- find
$$\int y ^ { 2 } \mathrm {~d} x$$