Complete solution in last part
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_ [2 sin(t) o (0)-5.5 a. Form the complementary solution to the homogeneous equation e(-t) 5e (t)...
Consider the initial value problem: 2' - 2+ 2(0) = (*) a. Form the complementary solution to the homogeneous equation. -e (t) = 21 +02 b. Construct a particular solution by assuming the form zp(t) = ae+ bt+c and solving for the undetermined constant vectors a, b, and c. 2p(t) = c. Solve the original initial value problem. 31(t) ) - 22(0)
I need help (2 points) Consider the initial value problem -,[0 1 y 1 0 -4 2(O) a. Form the complementary solution to the homogeneous equation. b. Construct a particular solution by assuming the orm УР t = a + t and solving or he undetermined constant vectors a and c Form the general solution (t) c(t)(t) and impose the initial condition to obtain the solution of the initial value problem. n(t) y2(t)
point) As an illustration of the difficulties that may arise in using the method of undetermined coefficients, consider 0 a. Form the complementary solution to the homogeneous equation. c(t)-c +, 02 ai -e®a, where a b. Show that seeking a particular solution of the form Walt s a constant vector does not work. In fact, if had this form, we would arrive at the following contradiction: d1 and a1- c. Show that seeking a particular solution of the form jp(t)...
(1 point) Solve y" + 2y + 2y = 4te-t cos(t). 1) Solve the homogeneous part: y' + 2y + 2y = 0 for Yh, using a real basis. Note the coded answer is ordered. If your basis is correct and your answer is not accepted, try again with the other ordering. Yn = C1 e^(-t)sin(t) +C2 e^(-t)cos(t) . 2) Compute the particular solution yp via complexifying the differential equation: Note that the forcing e * cos(t) = Re(el 1+i)t)....
<---- equation (6) Using the equation (6) in page 569 of our text, obtain the solution of ut-CUx -lx in integral form satisfying the initial condition u(x, 0) = e- 30 1 | [A(p) cos px + B(p)sin px) e-c2p2tdp 11 (x, t; p) dp= u(x, t)= 0 Using the equation (6) in page 569 of our text, obtain the solution of ut-CUx -lx in integral form satisfying the initial condition u(x, 0) = e- 30 1 | [A(p) cos...
1. Consider the Partial Differential Equation ot u(0,t) = u(r, t) = 0 a(x, 0)-x (Y), sin (! We know the general solution to the Basic Heat Equation is u(z,t)-Σ b e ). n= 1 (b) Find the unique solution that satisfies the given initial condition ur, 0) -2. (Hint: bn is given by the Fourier Coefficients-f(z),sin(Y- UsefulFormulas/Facts for PDEs/Fourier Series 1)2 (TiT) » x sin aL(1)1 a24(부) (TiT) 1)+1 0 1. Consider the Partial Differential Equation ot u(0,t) =...
Problem 1. Consider the nonhomogencous heat equation for u(a,t) subject to the nonhomogeneous boundary conditions u(0,t1, t)- 0, and the initial condition 1--+ sin(z) u(z,0) = e solution u(z, t) by completing each of the following steps Find the equilibrium temperature distribution we r) Find th (b) Denote v, t)t) - ()Derive the IBVP for the function vz,t). (c) Find v(x, t) (d) Find u(x, t) Problem 1. Consider the nonhomogencous heat equation for u(a,t) subject to the nonhomogeneous boundary...