What is the interpretation of Vx'(t)2 + y'(t)² for a particle following the trajectory (x(t), y(t))?

Q: - 2. (4)y=x'. D² +5D+

A: Given differential equation is, D2+5D+4y=x2.

Q: 3. t(t-4)y" + 3ty' + 4y = 2, y(3) = 0, y'(3) = -1

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) × r"(t). 1 r(t) = 2t²i – 4tj +t³k (a) r'(t) (b) r"(t)…

A: As per our guidelines we are suppose to solve only three sub-parts of a question. Kindly re-post the…

Q: If y(v) = V4+ a*dz then y'(v) =|

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Q: 5. (Dª – 5D² – 6D – 2) = 0

A: As per our guidelines we are allowed to do 1 question at a time. Please post other questions next…

Q: (b)Find orthogonal trajectory of x'y = c.

A: The given problem is to find the orthogonal trajectories of x2y=c.

Q: Determine y(t) Lly ✓ 3. y" 13y' + 40y = 0, where y(0) = 0, y'(0) = -2 -

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Q: The paths r(t)=(12, t3)" (t) = (t", t") and r1(t)=(t4, t6)"1 (t) = (e", t") trace the same curve,…

A: Given : rt=t2,t3 r1t=t4,t6

Q: Q1\ Answer (A) If y = sec(x), prove that y" + y = 2 y³ lo

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Q: y" (t) + 2y' + y(t) = 8t²e-t.

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Q: If r(t) = , find r '(t), T(1), r ''(t), and r '(t) ✕ r ''(t).

A: Given  r(t) = <4t, 6t2, 2t3>

Q: r(t) = 2t²1 - 4tj + 2t³k (a) r(t) (b) r"(t) (c) r(t)r"(t) (d) r(t) x r"(t)

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Q: If r(t) = (1,r ,t), then r'(t) equals (a) (1,21,-2r"). (b) (0,21,–21 ") . (e) (0,21,-21 *).

A: Given that: r(t)=1,t2,t-2Differentiate both sides with respect to…

Q: If r(t) = (6t, 212, 4t3), find r'(t), T(1), r"(t), and r'(t) x r "(t). %3D r'(t) T(1) = r"(t) = %3!…

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Q: |(3x + y') dx+ (2xy) dy C:ジャジ x² y² 3D1 16 from (3,0) to (0,4) 9.

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Q: 5) The position vector of a particle is given by s(t) = 2t² – 3t + 1.Find the time at which the…

A: answer = 2.5 sec   explanation is given in below step

Q: Suppose u(t) = w(t? + 4) and w' (5) = 11.

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Q: y'47y'+12y = 2le", y(0)=,0)=-10 .

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Q: Sketch the curve r(t)=f°i+tj and indicate the orientation. Find r'(t) and sketch r(1) & r°(1).

A: First we will plot the given parameters.

Q: Suppose r'(t) has units of m/s. Explain why T(t) = r'(t)/ | r'(t) | is dimensionless (has no units)…

A: Suppose r'(t) has units of m/s. To explain why Let r(t) be a differential vector valued functionNow…

Q: If r(t) =  , find  r'(t), T(1), r''(t), and  r'(t) × r ''(t).

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Q: y" - 2y' + y = 4e-t + 2et, where y(0) = -1, y'(0) = 2

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Q: If fx,y) = y'e e"+ then f,,(x.) =2y + Select one: True O True O False

A: Given   f(x,y) = y2e2x + (y3/x2)

Q: 4. Find dyax and d2 x =V4- t , go t²-2t ye t'-2 get'.

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Q: (x, y) = x + y' + kxy.

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Q: Find r'(t), r"(t), r'(t) r"(t), and r'(t) x r"(t). 1 t³ k 2 r(t) = 3t²1 – 3tj + 2 (a) r(t) (b) r"(t)…

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Q: С) хdy-у vdx-x²y°dy=0

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Q: d ef dt (F(=") = %3D dz dz 13

A: We have to find

Q: Solve (a) xy" - 3y' = x², (b) yy" + 2y'2 = 0, (c) y" + 4y = 0,

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Q: 3. (D³ +7D² +19D +13)y = 0 when x = 0, y = 0, y' = 2,y" = -12

A: What is Initial Value Problem: An initial value problem (IVP) in multivariable calculus consists of…

Q: 7. Find r(t) if r'(t) = 6e³ti r(0) = 5i + 3k. + costj + sec²t k and

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