Having laid out general theory of linear ODE (structure theorem \(+\) principle of superposition) we turn our attention to the specifics of solving linear ODE with constant coefficients. All such ODE can be converted to matrix-vector form. We first show how to exponentiate matrices using eigendecomposition: this settles questions about homogeneous ODE and complimentary functions. We then introduce the method of undetermined coefficients for constructing particular solutions of nonhomogeneous ODE whose forcing terms are combinations of elementary functions. Finally, we introduce convolution as a constructive way of computing particular solutions, first in one dimension and then in multiple dimensions. We use multidimensional convolution to derive impulse response of a mass-spring system which we then study experimentally for an equivalent RLC-circuit.