You are looking for a bounded solution that oscillates in time, so set the above constant to be pure imaginary. Show that if A = iw, where w > 0, then T(t) = Coeiut and X(x) = C1e(1+i)= + C»e¯X1+i)¤ for some real number y > 0. What is y? Hint: you will need to calculate Viw/k. Refer to Section 17.2 of the textbook if you have forgotten how to find roots of complex numbers

Q: Find y as a function of tif y(0) = 2, y'(0) = 3. y(t) = 0 16y" + 104y' + 169y = 0,

A:

Q: Find G'(w) if G(w) = 9 6 4w +6+ √w.

A:

Q: Find y as a function of t if: y''+8y'+97y=0 y(0)=9 y'(0)=3

A: Since the given differential equation is the second order linear homogeneous differential equation.…

Q: Find R(t) if R′(t)=⟨sint3,cost2⟩ and R(π)=⟨12,12⟩.

A: According to the given information it is required to find R(t).

Q: Find y as a function of tif y(t) T y" + 16y + 80y = 0, y(0) = 5, y'(0) = 2.

A:

Q: Find y as a function of t if y(0)= 4, y'′(0) = 1. y(t) = 25y" + 30y' +45y = 0,

A: given

Q: Let r(t) =(t, 1 − t,t2)Find the general formulas for T and N as functions of t

A: We have rt=t, 1-t, t2 Tangent vector is given as Tt=r't So, Differentiate the rt with respect t.…

Q: Let 7 (t) = Find 7'' (t)

A: given r→(t)=<-2t2-5,-4e-4t,sin(-3t)>formula used→(i)  d dt(tn)=ntn-1(ii)  d dt(eat)=aeat(iii)…

Q: Find y as a function of t if y(0) = 8, y'(0) = 4. y(t) = 6y" + 33y = 0,

A:

Q: Show that y1(t) = cos(3t) and y2(t) = sin(3t) are linearly independent for all t

A:

Q: Use linearization to estimate v26. Use L(x) = f(a) + f'(a)(x – a), where f(x) = vx and a = 25. Once…

A: Linearization formula L(x)=f(a)+f'(a)(x-a)

Q: Find r(t) given that r'(t) = and satisfies r(0) =

A: Step 1:  Step 2: Step 3: Step 4:

Q: ind the linear approximation of ƒ(x,y) = x³y² + 4xy at (1 and use it to approximate f(1.01, -2.01)

A: