13. [0.66/1.33 Points] DETAILS PREVIOUS ANSWERS Solve the wave equation a2. ax² u(0,t) = 0, u(L, t) = 0, u(x, 0) = x(L-x), = at² t> 0 ди at \₂ = 0 u(x,t) = 0 + Σ 0 < x 0 (see (1) in Section 12.4) subject to the given conditions. = 0, 0 < x
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- The parametric equation of the x_axis is t=1 O x=1 O x=0 O x=t2 PART B: ANALYSIS 1. Find the orthogonal trajectories of the family y = C'e". 2. Find the orthogonal trajectories of the family of circles r2 + y² = C.Q2) Solve the wave equation u=u 00 " XX 11 subject to u(0,t) = u(2,t) =0, t>0 and u(x,0)=0, u )=0, u,(x,0): = sin (3лx), 0Which of the following are parametric equations for the elllpse glven by +y'%3D17 Choose all that apply. Oz(t) = - 3 cos(t), y(t) = - sin(t) Oz(t) = 3 cos(t - 7), y(t) = sin(t– w) Oz(t) = 3 cos(5t), y(t) = sin(5t) O z(t) = cos(t), y(t) = sin(t) Dz(t) = cos(t), y(t) = 3 cos(t) O z(t) = 3 sin(t), y(t) = cos(t) O (t) = 9 cos(t), y(t) = sin(t) Or(t) = 3 cos(t), y(t) = sin(t)2. The position vector of a particle is given by r(t)= (2 cos t sin t)i +(cos^2 t - sin^2 t)j + (3t)k If the particle begins its motion at t = 0 and ends at t = pi, find the difference between the length of the path traveled and the distance between start position and end position3.8. Question. Match equations y' = sin x, y' = cos y, y' = y cos(x)· a) c) b) to direction fields. Justify.a2u satisfies the wave equation əx² -n a²u Verify that U(x, t) = e¬Vkt cos\ax %3D k at2Which is the graph of the derivative dy/dx of the parametric equations x(t)= 3cos t and y(t)=3sin t ,for Ost22n ? * of Option 1 Option 2 of Option 3 O Option 4Find the position vector for a particle with acceleration, initial velocity, and initial position given below. ä(t) = (5t, 6 sin(t), cos(3t)) 7(0) = (−2, —2, 5) 7(0) = (0, -4,0) F(t) = ( 5³ - 2t 6 > Question Help: Video Submit Question Search -6 sin (1) - 8t - 4 X cos(3t) + 5t+ W