Laplace transform of $$f\left( x \right) = \cos \,h\left( {ax} \right)$$ is

The analytical function has singularities at, where $$f(z) = {{z - 1} \over {{z^2} + 1}}$$

The value of the integral $$\int\limits_C {{{\cos \left( {2\pi z} \right)} \over {\left( {2z - 1} \right)\left( {z - 3} \right)}}} dz$$ where C is a closed curve given by |z| = 1 is

Solution of the differential equation $$3y{{dy} \over {dx}} + 2x = 0$$ represents a family of