4 | V1+y dy 3 ((1+9) GAC). ZV 2). 3 for KQuestion 6.6.13 -1/2 -x S= 27 V1- a21+ dx -1/2 r1/2 dx = 27. r1/2 x2 1/2 VI- x2. 1- x2 x2 1+ 1- x2 dx = 47 = 47 = 47

Q: x+2 Which of the following integrals is suitable to solve / - dx by partial fractional method?…

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Q: 1-² dx dy dz se ³ 1 xyz 2-fff(x+y+z)dy dx dz TL 3-fff₂y sinz dx dy dz 6 -2

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: 5 By separation of variables, Solve the following PDES- ²4 = 4 24 dx² dt² 0 o u(e,t) = u(s, t) =6…

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Q: Find the solution. Zy dx = (-1dx - dy) A (x-1)x = (y+1Xc - 2x - In|y-1|) B (x-1)y = (x+1Xc +x -…

A: First re-arrange the given differential equation. 2y dx=x2-1dx-dy2yx2-1=dx-dydxdydx+2yx2-1=1

Q: b) Golve: 4x°y*+4x°4- sx y' + 24= 60x?+8x +1 on Co,00) (2) vsing the Method of Uaniation of…

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Q: If y = f(x) is the solution of (4ay – 10x – 2y²)dx + (x4 +3y² – 4xy)dy = 0, f(0) = 0, then %3D…

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Q: 2. Integrate numerically the given function, fx0.1(1.2-x)(1-e20(x-1)) dx with the multiple-segment…

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Q: QI Find d for dt dy = 4e - 5x'e0 dx dy 3x e +5x'e dx الخبار ه 2 dy dy 2xe 2e + 4xe* dx dx dy 5x'ere…

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Q: 2. [e²v ycos (xy)| dx + [2xe2y (xy) + 2y] dy = 0 xcos - -

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Q: (- 1)"x" .n (– 1)"x2n (2n)! (– 1)"x 2n+1 V3 = = n=0 (2n + 1)! n =0 n! n = 0 is asolution for D.E

A: Note that, ∑n=0∞(-1)nxnn!=e-x∑n=0∞(-1)nx2n(2n)!=Cosx∑n=0∞(-1)nx2n+1(2n+1)!=Sinx

Q: Find the Generál Solution of thc D.E using only: y: v " or x = Yy" 1:) xydx - ( x* + 3 y² ) dy 2:)…

A: 1 xy dx - x2+3y2 dy = 0      xy dx = x2 + 3y2 dy       dydx= xyx2 + 3y2→ Take y = vx          dydx =…

Q: d & fle²- · *[e' – In(2t+1)]dt, find g''(x) . dx -2 If g(x) = - A B c) e*- D 4 et + (2x + 1)² e* -…

A: The Leibnitz rule for differentiation under integral sign is,…

Q: Q3 Find and show the work for (x+3)(3x+2) dx. (a) х (b) F (sin(2x) – cos x) dx. (c) S(3x² + 2x +…

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Q: Find the general solution of (1+ cosy)dx - xsin ydy = 0. a. X - sin y - x cos y = C b. x + sin y +…

A: The solution is given as

Q: 2. Find P.S. of when y (2x²-xy +y ²) dx − x²(2x-1) dy o y = 1/2. X = /

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Q: The DE whose general solution has the form y= C x+ Czxinx + C3x,x>0,5 gven by O C xy3)-2x²y"-3xy-3y…

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Q: Given : 6x³e** +3 dx. Using integration by parts (S udv = uv - f vdu) and letting u = f(x), dv =…

A: Given,           ∫6x3ex2+3dx

Q: kx 4+x² If k 1, evaluate k (a) 2 kx (b) 2 J₁ arctan (2x) + C arctan (2x) + C dx. (c) // ln(x² + 4) +…

A: Given: ∫kx4+x2dx We have to evaluate the given integral.

Q: In +1- 2 dt, if we let V Vt+1-2, then dt is equal to t+1– 2, then dt is equal to A) None 4x³dx ©…

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Q: To solve the equation y" – 6y + 8y = 2e*x + sin(x) + 3x² + 4, what trial particular solution should…

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Q: Q4 Find dy for all of : dx 3 x(x-2) 1- y = xvInx 2- у 3D x2+1

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Q: 2. gxc2x2+3 dx Selast & du 니 get x in terms of u ut 2x2 +3 4-3 = ㄹ x² 4-3 x = 이들 4-3 z soke har x…

A: Given ∫x2x2+34dx

Q: What is / - z dx? 1-x² o f- dx = -2cos-lx + C V1-x2 S- dx = 2sin-lx + C (1–x2 S-d 2 dx = 2cos-x + C…

A: 1. I=∫-21-x2dx =-2∫11-x2dx =-2sin-1x+C    ∵As ddx(sin-1x+C)=11-x2⇒∫11-x2dx=sin-1x+C=-cos-1x+C…

Q: Find the general solution of (y + 1)dx + (4x - y) dy = 0 Show your solutions on a separate sheet of…

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Q: dy бх + 2ху y(0) = -2V7 %3D dx -x² + 16 |

A: Solution: The objective is to find the solution of the given differential equation

Q: If g(x) = -S^*[e²− ln(2t+1)]dt, find g''(x) . dx 2 (A (2x + 1)2 Be* -In(2x+1) 4 (C) Ce¹+ (2x + 1)² 4…

A: Here is the solution of the given problem.  By using derives under Integral.

Q: Find the general solution of dy/dx = (x - 4) / (6 - 5x + x^2). O y = 2 In(x - 2) - In (x - 3) + C y…

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Q: 3 Given y = (1– V2x)°; Find dy/dx O dy :-3(1 – v22)? de O (E) None of the choices O dy 3(1 – V22)°…

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Q: Find the general solution of (x-4y)dx + (x+2y dy) = 0

A: Given

Q: Given: xe*² + In(x - y) = . Find dy/dx. 2xy(x-1 dy dx 20g/l) ta [1+(v)(22+1} ] x4+x²(x−y) Ody dx…

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Q: In x -dx C. d. 5% dx хе fx(2x +1)* dx е. f. In(x + 1)dx x2 dx Vx + 2 g. x4 h. dx Vx5 + 1 4 i. j. 1…

A: From the given problem:   c).   I=∫lnxxdx..1     Let,   lnx=uddxlnx=dudx1x=dudxdx=du Substitute…

Q: 3. Obtain the Particular Solution when x = 4 and y = 1 (x+ y - 4)dx - (3x- y – 4)dy = 0 %3D

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Q: Q1-Find dy / dx for the following functions : e0 -2 2.8ln2 Y: Cosh9x * Inxy 4 6. cos0 log2 2 Q2-…

A: By bartleby rules, only Q1 has been answered.  Given function is…

Q: In t+1-2 dt, if we let V Vt+1-2, then dt is equal to 4x(x²+ 2)dx B (4x³+2)dx None D 2(x²+2)dx E…

A: To find out the dt.

Q: Find solutions to the equation dt dX = k (a – X) (ß – X) governing second- order reactions in the…

A: We will use partial fraction method to solve the differential equation.

Q: dy _ 2y = x-'y¯1 y(1)= 3 dx

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Q: c3 Q3/ Evaluate , S(6x³ + 6y²) dx dy using Simpson's 1/3 rule in x-axis and Trapizodal rule in y…

A: Given ∫23∫466x3+6y2dxdy

Q: Find general solution of (x − 4y − 3)dx + (−x + 6y + 5)dy = 0 (DE WITH COEFFICIENTS LINEAR IN 2…

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Q: The standard form of 3dy-xydx= 3y³e/3 by Bernoulli's ec 4x/3 dx 3 A dy ху = 3e**/3y3 dx 3 'x=…

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Q: 4. Compute (a) 4 S"(3t2 – 4)z dx - dx 'x (b) x1+t² 4 dt dx -x 1+t2 d

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Q: dy If ey dx 3x2 and y (1) = 2, then the particular solution y (x) is, O y = ln(x³) + 2 O y = x³ + e²…

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Q: Solve the Bernoulli's DE: (x°y3 + 1) dx + x4y2 dy = 0.

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Q: If the substitution m = 2x - y was applied to the DE: (2x – y+1) dy + e2-dx = 0, the resulting DE…

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Q: 2 x2 Calculate the integral: dx (x – 4)² (x + 4) 극마 + 4| + 4 + x – 4 글 -스 + C 4 3 b) zlnk + 4\ + x-4…

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Q: 1. Determine the general solution of (x 3y )dx – x dy = U

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Q: 4. Find dy and Ay for y = 3VT-1+2x at r = 2 with dr = Ar = 0.2. %3D

A: The given equation is y=3x-1+2x. Given that x=2, dx=△x=0.2. Now,…

Q: 11) e3x = sin(x + 8y) %3D dy A) - dx 3ex 8sin(x + 8y) 24ex dy B) dx sin(x + 8y) dy sin(x + 8y) -3ex…

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Q: 1)Sf e* dx dy on the rigen R: x =. x=1. y =0 .y = 2 is : a) 1 B) -2 c)2 az 2) 2 for the function…

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Q: The general solution to the DE, (x^2+y^2-5)dx = (y+xy)dy, is * -0.5y^2/((x+1)^2) + 2/(x+1) +…

A: I have solved the differential equation with the help of exact differential equation.Given…