8T 3/2 /1+ 4t² dt A. 3 2 87 t3/2 /1 – 4t + 4ť² dt 3 В. 27(t – t²)/1+4t² dt с. 2 D. 27(t – t?)V1 – 2t + 2t/2 dt - 2 :| 27(t – t²)/1 – 4t + 4ť² dt Е. 8T F. | 13/2 /1 – 2t + 2t\/² dt 3

Q: are both solutions for the homogeneous DE: The functions y1 =e" and y2 =e y" - 16y = 0. Then, the…

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Q: Exercise : 4 3 a) Evaluate , S /1-х2 |1-x²-y² .-3(x²+y²+z²)² dz dydx

A: Triple integral is used to find the volume bounded by a region. There are many methods that are used…

Q: 3 (D² + 4)y = Ost<3 3t +2 t23 y(0)=0, y'(0)=1 Find L{y} L{y} = 1 3 3e-3s 8e-3s $2+4 s(s² +4) 2…

A: Laplace transform and formula

Q: What is the equation of the orthogonal trajectories of 4x + 5y = C? (1) 4х + 5у %3D k (2) 4х — 5у…

A: Given : Equation 4x + 5y = C To find : Orthogonal trajectories for the given equation?

Q: fa(4, 3) = 2, fy(4, 3) = -6, 6. dz find at t = 2 when x = g(t), y = h(t) and dt g(2) = 4, g'(2) = 2.…

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Q: dr = (t ) dr = (2, -1, 0) SF.dr 2 XYz1-X yJ +z°x K • <2,-1,07 SAXyZ +Xy dt 4 S4(2t)(-t)(1) +…

A: Yes answer is correct...

Q: 5(a) Determine the orthogonal trajectories of the family of electric field lines described by the…

A: To find - Determine the orthogonal trajectories of the family of electric field lines described by…

Q: A researcher wants to analyze the effect of a variable x on another variable y using observations…

A: Given the estimated model for the variables x and y as I yi=β1+β2xi+ei II yi=β1+γ1ri+β2xi+γ1xi…

Q: [1] Determine the orthogonal trajectories of y(1+2x?)=ax.

A: The given equation is:y1+2x2=axy=ax1+2x2              ..............(1)

Q: Use Gauss-Seidel method to solve for x, X,, Xạ until the relative error falls below 5% Repeat with…

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Q: Suppose that the share of total production consumed by player i is x / x+(n1)y, where x s player i's…

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Q: x²y" +xy' – y = T

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Q: Two identical very long rods are at different temperatures T| and T2. At time t = 0[ they are…

A: Given data:  T1 and T2are different temperature  ut-k2uxx=0, -∞&lt;x&lt;∞, t&gt;0 ux,0=T1,if…

Q: Suppose that the total cost (in dollars) of producing a product is C(x, y) = 50 + 7x2 + 8y2, where x…

A: Differentiate wrt x and y

Q: 2 4 find the orthogonal trajectories to c¯y y" = 4y´ + x´ 2 2 .... ..... ..... .....

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Q: 3 (D2 + 4)y =- Ost<3 3t +2 t23 y(0)=0, y'(0)=1 Find L{y} °L{y} = 1 3. 3e 3s Se-3s 82+4 s(s2+4) s (s²…

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Q: At time 0, M is deposited into Fund X, which accumulates at a force of interest δt =0.006t2. At time…

A: According to the given information, it is required to determine the value of m.

Q: g(x) = 4x3 12x + 6 with domain [-2, 2] g has --Select- at (x, y) = g has --Select--- at (x, y) = g…

A: g(x) = 4x3 -12x +6

Q: 3 (D² + 4)y = Ost<3 3t +2 t23 y(0)=0, y'(0)=1 Find L{y} °L{v} = T+4 + F(2+4) 3 3e 3s 1le-3s s(s² +4)…

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Q: SOWE FOR THE ORTHO GON AL TRAJECTORIES y² = 4x² (1-ex)

A:

Q: (2t - 4 0st<2 (D2 – 1)y =- 12 %3D t22 y(0)=0, y'(O)=1 Find L{y} L (y) = F1) 4 2e-2s 2e-2s %3D -…

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Q: Find the general solution of the 2nd order non-homogeneous DE using variation of parameters: y” -…

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Q: Solve y′′(t)+2y′(t)+2y(t)=H(t); y(0)=1 ;y′(0)=0 where H(t)=2t+3 , 0≤t<1 H(t)=3t+1, t≥1

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Q: A particle moves along the x-axis so that at time t\ge 0t≥0 its position is given by…

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Q: 5(a) Determine the orthogonal trajectories of the family of electric field lines described by the…

A:

Q: i) Let f(x, y, z, p,q) be a homogeneous function of degree n of X, y and Z. Show that the equations…

A: (i) Given that f(x,y,z,p,q) is a homogenous function of degree n of x,y and z. Let We know that to…

Q: The homogeneous equation with constant coefficients of least order that has y = 2e3t + 3 sin(3t) +…

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Q: (x + 2)-(x + 2)+y 3x +4 diferansiyel denkleminin genel çözümünü dx2 bulunuz. i riiniiz

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Q: dr = -4rt whent=0, r=r, dt Obtain the particular solution of - %3D

A: we have to use separation of variable

Q: The solution of y" = 8(t – 1) – 6(t – 3), y(0) = y'(0) = 0 is y(t) = %3D (A) (t- 3)[u(t - 1) - u(t-…

A: Given y''=δt-1-δt-3, y0=y'0=0

Q: Solve this.

A: Consider the following spring mass system.

Q: Find constant 3x 1 vectors u and uz such that the solution of the initial value problem 2 -4 -3 x' =…

A:

Q: C(x, y, z) = 90 + 6x + 4y + z where x is the cost of 1 pound of one raw material, y is the cost of 1…

A:

Q: Suppose that the total cost (in dollars) of producing a product is C(x, y) = 15 + 3x2 + 5y2, where…

A: C(x, y) = 15 + 3x2 + 5y2, x is the cost per pound for material and  y is the cost per hour for…

Q: The solution of y" = 8(t – 1) – 8(t – 3), y(0) = y'(0) = 0 is y(t) = (A) (t – 3) [u(t – 1) – u(t –…

A:

Q: 2) .. Use separation of variables to find the general solution.   dy dt − 12t3e−y = 0.

A: Answer: The solution is as given below:

Q: Use the backward Euler method with h = 0.1 y'(t) + 1000cos(y(t))-100t = 0 y(0) = -0.5   find y(2)

A: Given y'(t) + 1000cos(y(t))-100t = 0 y(0) = -0.5and h = 0.1

Q: 7x + 5y + 9z- 8t dy = 4x + y+ z + 2e-t dt dz dt - 2x + 3y + e-t - 3t = 7x + 5y+9z - 8t dt dy = 4x +…

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Q: 2t-4 0st<2 (D2 - 1)y = t22 y(0)=0, y'(0)=1 Find L{y} L (1) = 1 + - - 2+ 4 2e 2s 2e-2s %3D | L (y) =…

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Q: Use the method of variation of parameters to produce a general solution of the inhomogenous equation…

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Q: At time 0, M is deposited into Fund X, which accumulates at a force of interest δ# = 0.006t*. At…

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Q: 1 y" – 2y' + 2y y(4) = 0, 3 (4) = 0. -

A: Given: The given differential equation is y''-2y'+2y=1x, y4=0,y'4=0

Q: SOLVE FOR THE ORTHOGONAL TRAJECTORIES X'(3k-x) - ky = xy

A: Take first derivative and eliminate k.

Q: 3- Find the orthogonal trajectories of a system. x²y² – 2xya + a = 0 %3D

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Q: f(x) = 2x5 + 15x4 - 3x3-4x2+ 7x+ 14 1)Trapeaoidal rule 2) Trape20idal rule with n=2 3) 1/3 Simpson…

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Q: If u(x, t) = E1 fn (t) sin(næ) is the solution for Utt + 9uz = 2e" sin(3x) + e sin(4x) u(0, t) = 0 =…

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Q: (x, y) - arty! - b where x is the amount of money expended on labor, y is the amount expended on…

A: Solution is below

Q: t3 – 1– 2vt - f(t) = -t5 2 f'(t) : t3 5 %3D Vt11 t6 2t3 – 5 – 9VE f'(t) = t6 7t3 – 9VE f'(t) t6 9 5…

A: f(t)=t3-1-2t-t5