In this talk, we present some recent quantum algorithms to solve linear differential algebraic equations. These are linear ordinary differential equations with algebraic constraints. We present quantum algorithms that solve these equations and we also characterize conditions under which the run-time is efficient, i.e., polylogarithmic in the number of variables. We then apply the quantum algorithm to simulate large RLC (resistor-capacitor-inductor) networks with current or voltage sources. We show how to estimate certain observables such as energy in a subset of capacitors or inductors in these networks. We will also present a quantum algorithm for integro-differential equations or differential equations with memory. Here the quantum algorithm can simulate such equations under a condition we call “short-term memory”. For certain integro-differential equations, however, one can exploit additional structure and simulate the equations even when the short-term memory condition is violated. We give some examples of such equations and the quantum algorithm to solve them.