4. For each of the following IVPs, find the general solution of the ODE and use it to solve the IVP: (a) d²u dt² du dt +2- +u = 0, u(0) = 1, du dt (0) = 0

Q: alculate the first six iterates for the equation x = e. When xo 0.

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Q: find dy/dt.

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Q: In 2 I = t-2 e(-1/t) dt

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Q: a - Find h (Stet sinh t sint dt)

A: The objective is to find ∫te-3tsintsinhtdt It is known that, sint=et-e-t2isinht=eit-e-it2…

Q: dy 9. = 2+ e dt

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Q: v = ) V In(2x-3y

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Q: Find two solutions for the below ODE. Why can you not use the existence and uniqueness theroem for…

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Q: find dy/dt. y = (esin (t/2))3

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Q: Y(3x*2)dx + x (1-2y) dy-0

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Q: dp apš – Bp dt p(0) = 0

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Q: Solve for x: X S₂ 14 2 1 t(4- t) dt= 0.5, where x € (2, 4).

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Q: Find the second differential of the function y=x2cos2x.

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Q: dv * + 4v = 0 dt

A: We have given differential equation,     We will find solution using separable method.

Q: dT +kT =200k, where k is a constant. dt Solve A. T=ce" + 200 B.T= ce–200 C. T=ce +200 D. T= ce"+200e…

A: See the detailed solution below.

Q: az or and as dz az Using the given information, determine dt 3. at az = 2 ax az dx dy =1, ду (a) 4…

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Q: If s=5√t+4, then ds/dt =

A: Given s=5t+4

Q: Ex.: Solve dx dy 2=t.... dt dt dx dy -+2 +2-y=0... y = 0.. dt dt

A:

Q: If A = 4x³ and (a) TRUE (b) FALSE dt dx 2, then dA dt = 150.

A: As we know the Power law; ddxxn=nxn-1 Given: A=4x3 and dtdx=2

Q: Solve dx dt = = et cos(2t) + t with x(0) = 3.

A: Step 1:Step 2: Step 3: Step 4:

Q: dt K = t5

A: Given : K = ∫15dtt5

Q: relate dI/dt to dT/dt the answer is dl/dt= dI/dT x dT/dt

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Q: Calculate G(16), where dG/dt =t-1/2 and G(9) = -5.

A: