$$\frac { \mathrm { d } ^ { 6 } y } { \mathrm {~d} x ^ { 6 } } = k \frac { \mathrm {~d} ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }$$
where \(k\) is a constant to be determined.
Hence determine the first 5 non-zero terms in the Maclaurin series expansion for \(y\), giving each coefficient in simplest form.