(D² – 3D – 4)y = 0 is ° y = C,e** + C,e* " y = C,e** + C,e* 4х 4x -X -4x ° y = C,e** + C,e* y = C,e* + C,e* -x -4x

Q: 24. Evaluate x² dx + yz dy + (y²/2) dz along the line segment C joining (0, 0, 0) to (0, 3, 4).

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Q: af dy %3D Y Given f(x, y) = 17x² sin y then 17x2 cos y O -34x cos Y O -17x² cos Y 34x cos Y II

A: The function is given by fx,y = 17x2siny To evaluate : The expression of ∂f∂y

Q: $5y dx + 4x dy,where C is the square with vertices (0, 0), (2, 0). (2, 2), and (0, 2) oriented…

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Q: 5. y" + y = 2t, y(1) = 1, y'(1) = -2, yp(t) = t² – 2t 6. y" + y = 2e-', y(0) = 2, y'(0) = 2, yp(t) =…

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Q: Given: a = 0 – sin 0; y= 1- cos 0 d'y Find: dz2 O d'y 1 dz2 (1-cos 0) d'y 1 %3D dz2 (1-cos 0) O dy 1…

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Q: 2) (1+ e*/y)dx + e*/y (1 – 2) dy = 0 Ans: x + ye*ly = c (Bali, 2007) %3D

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Q: dz at (и, v) — (1,1) if du Use chain rule to find || a(w² - z + 1)-), : x = 3u – v, y = u°. 2 = x…

A: According to chain rule of differentiation . According to power rule of differentiation .

Q: y In x – x In y = 4, y' y In (x² + y² )= 2 arctan 2) = 2 arctan y'

A: This question can be solved using the concept of differentiation of implicit function.

Q: Y = w tan-1(uv), u = r + s, V = s + t, w = t + r when r = -1, s = 2, t = -1 1. as at ar as %3D

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Q: 2, 0 1

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Q: homogeneous y". 2y". uy's8ys nd soluti on L'inear ODES No7 - 3x e +8x?

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Q: 3. 다음 함수 /에 대하여 /w, /w 를 각각 구하고 비교하 여라. (1) f(x, y) = sin' xcosy (2) S(x, y) = 2x²+5xy+ y² %3D (3)…

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Q: 2- Linear edluan 1 - y' +スリ= 2é 2- x y'ony-ax? %3D 3. (x-2) y`+y. x 4 4-(49-3x)dX+5X dy = - 5_ dy dx…

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Q: Exact difterential egation 4. (1+In(xy))dx+ 1+ dy=0 y,

A: Given differential equation is, 1+lnxydx+1+xydy=0   ...................(1) Comparing with Mdx+Ndy=0…

Q: ex+y ди 21. If u = show that ax ди = u ду - ex+ey'

A: The given function is: u=ex+yex+ey

Q: dy = (x + y +5)² is separable. dx The ODE %3D اخترأحد الخيارات ias O

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Q: (4, w/8) 1. (y cos xy dx + x cos xy dy) (0,0) (0,5) 2. e2* dx + ye2 dy) (5,0) (1,1) 3. 2(x dx +y dy)…

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Q: ( w"-y+ (x+ ¥)'y = In (금 + z) y(-}) = 1, y' (-}) = o %3D

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Q: dy -y2+1,ysCJse Cantial cokditian.

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Q: (а) у'-у%3D0 (b) y" – 9y=0 d y d'y (c) dx? dy +2 dx = 0 dx (d) dx² = 0 (e) 2D’y-13D +15y=0 () 3D'у…

A: As per our guidelines we are supposed to do only first three subparts. Sp please upload the other…

Q: z = In (VT" + y") If With n e N, n > 2, Then the result of 2 (dz dy dz n Corresponds to: "-1 + y"-1…

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Q: The standard form of 3dy-xydx= 3y%e*/3 by Bernoull's equation is: dx A Зе dy xy = 3e**/3,3 dx 3 x-…

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Q: (d) S (1, y) = sin (2), (x, y) # (0,0) 0, (x, y) = (0,0) (e) , r + y # 0 7+y x² + y = 0 0, f (x, y)…

A: Limit of a function: A function f is said to tend to a limit l as a point x, y tends to the point…

Q: re' dy + +1 dr =0 O (y – 1) e + + In z = C 2. O-(y+1) e + Ine =C 2 O (1- y) e + 1. O 2y - e + +In=C

A: To solve given differential equation

Q: dy If ex+У%3D ху, then dx %3D Ух- 1) A x(у- 1) (1- x) B x(y- 1) x(у- 1) Ух- 1) x(1-у) (D y(x- 1)

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Q: se Green's Theorem to evaluate SC (5y-9x)dy-(yx-x³)dx where C is shown below

A: Follow the procedure given below.

Q: Y 30 ΨΥ Ỉ2 2 47 13 23 24 με χ ΕΙΝΑΙ Fino η Exy. ἐκ ἔγ In ex² - (Ex)^ in [y- (fy) th nexy- έχτι…

A: Given information: X Y X^2 Y^2 XY 27 30 729 900 810 44 19 1936 361 836 32 24 1024 576 768…

Q: Find the general solution of the ODE below. 2z y'" – 4y' + 4y = e" arcta y(x) =

A: Introduction: If a second-order homogeneous differential equation has two equal real roots, then the…

Q: 1. The loop of y² = x * (4 - x) 2. у %3D 6х — х?, y = x² – 2x - 3. у %3D 2х y2 + 4x – 8 = 0 - 4. An…

A: Question 4 : Arch of y = (1/3)sin(x/3) First find out intersection points :  y = 0 (1/3)sin(x/3) = 0…

Q: Slp xeydydx R= {(xy)|(0<x<1),(0<ySx²)}; R = limits %3D а. 2е + 1 b. ;-1 e 2 С. e + 2 d. None of the…

A: We have to evaluate integral.

Q: hich of the following is not variable separable? (А) 2ху dx + (х2 + 1) dy %3D0 A ye' dy - (e-y+…

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Q: obtain the family of solutions [x − y arctan (y/x)]dx + x arctan (y/x) dy = 0

A: The detailed solution is given below Thank you

Q: dz at (u, v) = (1,1) if du Use chain rule to find -z + 1);), = x = 3u – v², y = u® z = x sin( (y? |…

A: If the input of the function is more than one, then it is called a multivariable function. In this…

Q: Evaluate ff, xy.cos yz dx. dy. dz D = { (x,y, z): 0 <xS1 & 0<ysl & 5:50

A: We have to evaluate ∭Dxy⋅cosyzdxdydz, where D=x,y,z:0≤x≤1 and 0≤y≤1 and 0≤z≤π2 Now,…

Q: 3. [cos y + 1]dy + [tan x (sin y + y)]dx = [sin y cos x + y cos x]*dx gettyimages Fuse When:x = 0; y…

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Q: S, (x + 2y) dx + x dy. C consists of line segments from (0. 0) to (2. 1) and from (2, 1) to (3, 0)

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Q: 14. Evaluate 4y dx +3ax dy, where C is the trapezoid with vertices (0,0), (2,0), (6,2) and (0,2).

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Q: 2. y' = y sec x ; 3. у(3x3 — х + у)dx + x?(1 — х?)dy %3D 0 4. у(2х — у + 1)dx + x(3x — 4у + 3)dy — 0…

A: 2) y'=y secx this can be written as dydx=y secx⇒dyy=secx dx integrate the function ∫dyy=∫secx dx…

Q: 1 If y = sin' x then is dx dy dy -3 cos x b) dx a) –3 sin² x cos x dx sin¯ x dy dy _ -3cosx = -3…

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Q: Can you please check my work for question 14? I know it it hard to follow, but I don't know if I got…

A: The given equation is,

Q: finde general Sonotion 1- y' = See'y 2X-1 %3D 2- 3-Xy=Y+2x $ in?

A: This question can be solved by applying the concept of differential equation.

Q: xy*-dy = (a* lIn a – y (а* In a - y %3D

A: we have to find the differential of ax=y

Q: 1.) 201 4sin (x) cos (x) dx dy 0 y² + 1 [¹ylnª (y² + 1)

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Q: 24. Evaluate . (x – y) dx + (x + y) dy counterclockwise around the triangle with vertices (0, 0),…

A: Given integral is, It can be represented using Green's Theorem as,

Q: Obtain a family of solution 1. [x-y arctan(y/x)]dx + x arctan (y/x)dy = 0

A: Solution is given below:

Q: -a+ito + DNE - 十→f -2 1 DNE + DNE - -1 DNE DNE | -1 1 2.

A: The function f is increasing on some interval, if f'&gt;0 on that interval.    The function f is…

Q: d²y then dx² cos x 2 dy Show that if y -+y = 0 x dx %3D

A: Given: y=cosxx To show: d2ydx2+2xdydx+y=0 Differentiate y with respect to x using the quotient rule…

Q: Evaluate 2.xyz dx + x²zdy +x²ydz over the path r(t) = (t², sin(nt/4), e'“-2') for 0 <t<2.

A: The given integral is: I=∫C 2xyz dx+x2z dy+x2y dzOver the path:  r(t)=t2,  sinπt4,  et2-2t    for…

Q: Find Particular Sol. of  xsin2 ycosy y' + sin3y/ 1+lnx = 4 ; y(e)= π/2

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