2. The speed of a particle at an arbitrary time t is given by || V(4t - 1) +sin? rt. Then V.d at t = is T (A) - (C) T (D) -т (E) 2 (F)-2m.

Q: 2. Evaluate: (a) L{t – cos 4t + e-3t sinh at} (b) L{U(t – n) + cos 6t U(t – 1/3)} 2s + 14 (c) L…

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Q: 1 Vx + 10 — о(х), х — 0 te-2n 10n В. о(1/п), п — о 1 — о(е "), п — sin æ = x- +0(x°), x → 0 3 D. n2…

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Q: 1. Show that if you differentiate both sides of x2 + 2y³ = 6, the result is 2x + 6y2 = 0. Then solve…

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Q: d² dx dx 3. di² +2 +5x = sin 21, given that when t = 0, x = 3 and dt dt 53 [ 55 Ans. e 17 cos 2t + -…

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Q: Find a general solution to the given Cauchy-Euler equation for t> 0. By"(1) – 3ty'(t) + 4y(t) = 0…

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Q: (d) Finally, show that the conditions for the theorem are not satisfied for the initial value…

A: (D) here fx,y=y13 differentiate it with respect to x ∂f∂x=13y-13dydx initial condition y0=0

Q: Consider the initial value problem sin(t)y" - ,y + r*y= In -, y(3) = -1, y'(3) = 57. Without solving…

A: Uniqueness and existence theorem: Let p, q, and g be continuous functions on an open interval I such…

Q: A particle moves along the x-axis so that at any time t, t 2 0, its acceleration is a(t) = -4…

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Q: By using first fundamental theorem of calculus. Solve the problem 1.) Suppose f(x, y) = S*3 If fx…

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Q: 2. Consider the initial value problem (IVP) { (t +1)(t – 1)(t- 2) t e"y y(.5) - cos t? %3D 1 Use…

A: Furst we rewrite the equation as in the theorem, then Use the given theorem

Q: I. Obtain the general solution of the following: D. (3D2 + 12)y = tan x E. (D2 − 3D + 2)y = cos…

A: We have to obtain  general  solution of given differential equation.

Q: Determine the largest interval in which the unique solution of (t-3)y +tan ty t, y(m)=0 is certain…

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Q: Given that x(t) = c¡ cos wt + cz sin wt is the general solution of x" + w²x = 0 on the interval (-*,…

A: 10 Given solution of differential equation is x(t)=c1cos ωt+c2 sinωt of the differential equation…

Q: IV. Suppose z is a function of x and y, and tan yy² + x² = z*e6y. Solve for dz dz and

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Q: 2. Find L{f(t)} if f (t) = = cos 4t + t-1/2 + e5t – sin 3t – 5t – 1.

A: We will use the formulas Lcos at = ss2+a2Leat = 1s-aL(sinat) = as2+a2L(tn) = n!sn+1 Hence we have…

Q: Solve the following initial value problem y' + 4y = g(x), y(0)=1 and y'(0)=2 where g(x)is defined as…

A: According to the given information, it is required to solve the initial value problem.

Q: If ä – i – 6x = 0 with x(0) = 1 and (0) = a, determine the value(s) of a such that the solution…

A: Given,        x¨-x˙-6x=0   with  x(0)=1    and    x˙(0)=a

Q: 12 Solve the boundary-value problem du 0 0 at + sin x %3D u(0, ) = 400, u(T, t) = 200, r>0 u(x, 0) =…

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Q: 4. g(t) = e³t + cos(6t) – e³ªcos(6t) 5. f(t) = tcosh(3t) 6. h(t) = t²sin(2t)

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Q: 5.. Find the general solution to the DE using the method of Undetermined Coefficients: y" – 4y = te'…

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Q: 4. Solve the following equation by backward Euler's method and also trapezoidal method: 1 1+t² y'…

A: Introduction: There are many iteration tools that are used to solve an initial value problem…

Q: A yoyo bounces up and down in the vertical direction with its acceleration after tt seconds given by…

A: d^2y/dt^2 = a(t)

Q: 5 By separation of variables, Solve the followin PDES :- du dt d2u dx2 @ o U (0₂t) =(4,t) = G u(x,0)…

A: Given is the Partial Differential equation ∂u∂t=2∂2u∂x2…

Q: 5. Find a general solution to the following nonhomogeneous equation: 1 y" + y' cos t sin t Hint: S…

A: Third order non homogeneous differential equation.

Q: 2 1 e. Use your answers for parts c and d to estimate -dx using Simpson’s rule with n=8 1+x

A: We have to find the integral by Simpson rule

Q: 22) Use Euler method to estimate the solution of the ODE y' (xy?) ,y(1) = 2, h = 0.1 at x = 1.2

A: using the Euler's rule: yi+1=yi+hf(xi,yi) we will find the solution of given ODE we have…

Q: Solve the initial value problem. ds = Cos t - sin t, s dt = 4 %3D

A: According to the company policy, I'll solve the first question. Please resubmit the second question.…

Q: or the following IVP, determine the t-interval (a, b) on which Theorem 2.1 guarantees a unique…

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Q: Determine the largest t-interval on which the initial value problem (sin t)y - 2ty=0 y(2) = 1 is…

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Q: Solve the following using Exact, Linear or Bernoulli's solution. 1. cos(x + y) dx + (3y² + 2y +…

A: Given:            cos(x+y)dx+(3y2+2y+cos(x+y))dy=0;      y(1)=−2.

Q: a. Solve the initival value problem: y = 5 cos (2r)/(6+ 5y), y(0) = -1. -6+V36 - ( sin (x) + 10 2. A…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 7. Obtain the particular Solution by satisfying the conditions indicated. 3x dy; when x = 2, y = -1.

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Q: 5. Find the General and Particular solution of 2 = 3y ; y = 3, when x = 0 dy dx

A: We have dydx=3y Now, we can write this as: dyy=3dx Now, integrate both sides: ∫dyy=∫3dx⇒lny=3x+C…

Q: Solve the D. E. to the I. V. P. sinx(e¬ + 1)x' – cosx = 1, y(곡) = 0 - O (1 + e') (1 + cos x) = -1 O…

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Q: Find the solution to ty' + y = sin (5 t) satisfying y5 1 == and valid for all t> 0.

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Q: 1. [8te" dt 2. . (1–3x)sin(}x)dx 3. w'e*™ dw 1-1

A: "Since you have asked multiple questions, we will solve the first question for you.  If you want…

Q: Solve the following initial-value problem: V3 V1-y? dx - V1- x² dy=D0; y(0) = 2 O 2sin-1x+sin-ly=t/3…

A: Given: The differential equation 1-y2dx-1-x2dy=0 and initial condition y0=32, To Find: Solution of…

Q: 3. (1+ 2y²)y' = y.cos (x) diferansiyel denkleminin türü nedir?

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Q: Find the general solution using the method of variation of parameters of the following: (2) y" – 3y'…

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Q: Determine the longest interval in which the initial value problem (8t + 6)y" + 3ty – 4y = 3 cos(t),…

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Q: 4. Solve the following equation by backward Euler's method and also trapezoidal method : y'(t)…

A: Given differential equation is y'(t)=-10y(t)+11+t2+tan-1t,  y(0)=0, h=0.1, 0≤t≤0.2 Let…

Q: Solve the following differential cquations 1. x + x*y -sec(xy) Ans. sin x = 2x2 +C x +y Ans. y- tan…

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Q: 1. f(t) = cos(6t) 2. f(t) = (e^(8t)) cosh(3t) 3. f(t) = (t^2) e^(-4t)

A: Lcos(at)=ss2+a2 Leatcosh (bt) = s-a(s-a)2-b2 Ltneat = n!s-an+1

Q: solve the Cauchy problem on the real line for the given initial position and velocity functions and…

A: Given that, and ,  By the Cauchy problem ,

Q: d²y + 9y = 2 cos(3x); y(0) = 0; y'(0) = %3D dx² 3

A: Given differential equation is The associated auxiliary equation is Complementary function of…

Q: 24 Show that the solution of equation satisfying the condition O T-0, as t0 (1) T-0, for x-0 and x=a…

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: Exer 1. Solve the following first-order boundary value problem 2 u +4 u, + 40 u = u(z, 0) = e* 60…

A: We have to find solution of given pde

Q: Determine (without solving the problem) an interval in which the solution to the following initial…

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Q: The first approximation P of the solution to the equation f(z) = x² – 8 that is near to Po = 4 using…

A: As we know that the iteration formula of Newton's method is:   Pi+1=Pi-fPif'Pi  i=0,1,2,3.....…