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We present quantum algorithms for linear and nonlinear differential equations where we improved the applicability and efficiency of prior quantum algorithms. For linear ordinary differential equations, we show that the run-time can be bounded by the so-called exponential norm which leads to a more accurate characterization of the condition number of the resulting linear system. We discuss the application of these algorithms to the problem of coupled oscillators with damping improving on prior work. We then present quantum algorithms for nonlinear differential equations with applications to optimal control.