The inverse Laplace transform of $${{\left( {s + 9} \right)} \over {\left( {{s^2} + 6s + 13} \right)}}$$ is

Let $$\,\,f\left( x \right) = x - \cos \,x.\,\,\,$$ Using Newton-Raphson method at the $$\,{\left( {n + 1} \right)^{th}}$$ iteration, the point $$\,{x_{n + 1}}$$ is computed from $${x_n}$$ as

The solution of a differential equation $${y^{11}} + 3{y^1} + 2y = 0$$ is of the form

The differential equation $${y^{11}} + {\left( {{x^3}\,\sin x} \right)^5}{y^1} + y = \cos {x^3}\,\,\,\,$$ is