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FirstOrder Differential Equations
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air resistance approximate the solution assume auxiliary equation capacitor Cauchy-Euler equation Chapter circuit compute constant coefficients damping dependent derivative determine df/dy differential equation direction field dM/dy dN/dx dy dx dy/dx equa equation of motion equilibrium exact Example exponential Figure first-order equation formula fourth-order Runge-Kutta function given graph Hence Hint homogeneous equation implicit solution improved Euler's method independent variable inductor initial conditions initial value problem inside the building integrating factor interval isoclines kg/L L/min linear equation linearly independent logistic m/sec mass N-sec/m Newton's second law nonhomogeneous nonlinear numerical object obtain ordinary differential equation oscillator particular solution phase plane population procedure RC circuit roots salt satisfies Section separation of variables Show solu solution curve solution to equation solve step size h subroutine substitution superposition principle tank Taylor series temperature inside term Theorem tion trajectories undetermined coefficients unique solution voltage Wronskian y)dx yp(t zero