Linear of Differential Equations 4口14①yt至2000 Linear of Differential Equations
Linear Systems of Differential Equations Linear Systems of Differential Equations
Systems of Differential Equations So far,we have studied the differential equation that in- volves an unknown function and derivatives of this function. 4日0,1无2000 Linear of Differential Equations
Systems of Differential Equations So far, we have studied the differential equation that involves an unknown function and derivatives of this function. In this chapter we shall deal with sets of simultaneous equations that involve several unknown functions and their derivatives. Example d 2 x1 dt 2 −2 dx1 dt − dx2 dt = −3e 3t , dx2 dt −6x1 = 0. Linear Systems of Differential Equations
Systems of Differential Equations So far,we have studied the differential equation that in- volves an unknown function and derivatives of this function.In this chapter we shall deal with sets of simultaneous equations that involve several unknown functions and their derivatives. 4日10,1无2000 Linear of Differential Equations
Systems of Differential Equations So far, we have studied the differential equation that involves an unknown function and derivatives of this function. In this chapter we shall deal with sets of simultaneous equations that involve several unknown functions and their derivatives. Example d 2 x1 dt 2 −2 dx1 dt − dx2 dt = −3e 3t , dx2 dt −6x1 = 0. Linear Systems of Differential Equations
Systems of Differential Equations So far,we have studied the differential equation that in- volves an unknown function and derivatives of this function.In this chapter we shall deal with sets of simultaneous equations that involve several unknown functions and their derivatives. Example x1_2d_de=-3e, 2 dt dt -6x1=0. 4口14①y至元2000 Linear of Differential Equations
Systems of Differential Equations So far, we have studied the differential equation that involves an unknown function and derivatives of this function. In this chapter we shall deal with sets of simultaneous equations that involve several unknown functions and their derivatives. Example d 2 x1 dt2 −2 dx1 dt − dx2 dt = −3e 3t , dx2 dt −6x1 = 0. Linear Systems of Differential Equations
Example Consider the system of two masses and two springs shown in Fig5.1.1,with a given external force f(r)acting on the right- hand mass m2.We denote by x(t)the displacement (to the right)of the mass m from its static equilibrium position(when the system is motionless and in equilibrium and f()=0),and by y(r)the displacement of the mass m2 from its static position. Thus the two springs are neither stretched nor compressed when x and y are zero. 4口14①yt至2000 Linear of Differential Equations
Example Consider the system of two masses and two springs shown in Fig5.1.1, with a given external force f(t) acting on the righthand mass m2. We denote by x(t) the displacement (to the right) of the mass m1 from its static equilibrium position (when the system is motionless and in equilibrium and f(t) = 0), and by y(t) the displacement of the mass m2 from its static position. Thus the two springs are neither stretched nor compressed when x and y are zero. Linear Systems of Differential Equations