Find the value of the constant \(k\) for which \(k x ^ { 2 } \mathrm { e } ^ { 5 x }\) is a particular integral of the differential equation
$$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } - 10 \frac { \mathrm {~d} y } { \mathrm {~d} x } + 25 y = 6 \mathrm { e } ^ { 5 x }$$
Hence find the general solution of this differential equation.