If z = x2 – y2 and x t cos 2r and y = r sin t, then %3D a2z is ar2 (A) 2 cos (2r) + 2r? cos?(t) – 2ry sin t (B) -8tx cos 2r + 8t2 sin 2r + 2 sin? t (C) 2 cos (2r) – 2r? cos (t) + 2ry sin t (D) -8tx cos 2r + 8t?sin2 (2r) - 2 sin? t | (E) -4x sin 2r - 2t sin 4r + 2y cos t +r sin 2t

Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler or Runge-Kutta method, what is…

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Q: Find the general solution. 1. (2xy-3x2)dx + (x2+2y)dy=0

A: According to company rule we can answer only first question and rest can be reposted

Q: The general solution of y" + 16y = cost is: Select one: a. y = C,cos(4t) + C2sin(4t) + cost 15 O b.…

A: A detailed solution is given below.

Q: 9.lf y = sin (4x – 5), then what is y'? O A. y' = - cos (4x – 5) O B. y' = - cos (4x) O c. y' = cos…

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Q: B.S(cos x + cos 5x)dx D.S(cos x – cos 5x)dx A.S(sin x + sin 5x)dx C.S(sin x – sin 5x)dx 8. S sec³x…

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Q: Find the general solution of 2ey cos 2x dx + (ey sin 2x + 3y sec2 y2)dy = 0. a. e sin 2x +y tan y? =…

A: This question is related to differetial equations, We will solve it using given information.

Q: 5- for y = (x² + 1)5 dx a)10(x² + 1)5 b) 10x(x² + 1)* c) (x² + 1)* 6- Sin 2x is equal to: a) sin x…

A: Answer of the above questions are

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: The general solution of the DE y"+ y = x is def ined by (y= C¸ cos(x ) + C¸ sin (x) +x 2 (y=C¸ cos…

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Q: 1. S cscxln(cscxsinxcosx)dx secx 2. ( 4sinx+sinxsecx cos²xv4+secx 3. ( sin(cos3xsin3xcsc3x)dx…

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Q: The general solution of y"+ 16y = cost is: %3D Select one: a. 1 y = C,cos(4t) + C,sin(4t) + Cost 15…

A: Given differential equation y''+16y=cost We have to find the general solution of the given…

Q: Let e4 – sin(x + y²) – VTY. Match the following. A. 4e - cos(x + y*) - | - 2 ay B.-2 cos(x + y²) +…

A: Given,f(x,y)=e4x-sin(x+y2)-xyDifferntiating both the sides w.r.t. x…

Q: y' cos x + y sin x = 2cos³x sin x- 1 What is the particular solution when y(T/4)=3v2 ?

A: Given differential equation is y'cosx+ysinx=2cos3xsinx-1 we have to find the particular solution…

Q: Find the general solution of sin x cos^2 ydx+cos^2xdy = 0  a. secx + tan y=C b. cos x cos^2 y + y…

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Q: The solution of the nonhomogeneous DE y" + y = sec?x is O None of these y = c1cosx + c2sinx +…

A: The given DE is, of the second-order and it is y''+y=sec2x which is non-homogeneous DE. So, first we…

Q: 1. If x - y = 25, then y" = c.) d.) - a.) b.) 2. If y = cos(3x+1), find y a.) 3 sin(3x+1) b.) -3…

A: Authoring guideline: As per the authoring guidelines, we can solve only the first three parts.…

Q: cOs x dx |(sin? z + 4)%/2 1 sin x sin x cos x 1 cos x +c +c 16 vsin ²x + 4 48(Vsin ²x + 4 16 Vsin 4x…

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Q: fz = 24 - 2x - 6y, x = cos(4t), and y = esint, then dz dt is equal to O-2 sin(4t) - 6esint cost O2…

A: Differentiate wrt t

Q: Find the general solution of (cos cos y + ycos x ) dx + (sin sin x – x sin sin y ) dy = 0 А. X cos y…

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Q: 22. If y = x+4 then what is 4Y? dx dy a. 4x(x + 4) dy С. dx -4Vx + 8 dx dy b. dx =-4(x + 4)= d. dx…

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Q: a. Find the General and Particular solution of dy/dx = −8 sin 4x ; y = 6 when x = 0

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Q: (. 0) S(x, y) = In(x² + xy), at (4, 1) S(x, y) = sin (x²) + cos y, at

A: 19. f(x, y)=sin(x2)+cos y At π2, 0, fπ2, 0=sinπ22+cos 0                =sinπ4+cos 0…

Q: 22 3x'y = 2ty- 3). 23 (2y cos x + sin* x) dx sin x dy; when x Ans. y= cty- 3) exp (x n, y = 1. %3D…

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Q: 32. a. b. f cos(4sinx - 1) cos(2sinx + 8) cosx dx is sin(6sinx + 7) − sin(−2sinx + 9) + C 1 1 12. 1…

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Q: Find the general solution of (1+cosy)dx-x sin ydy = 0. (1) x – sin y – x cos y = C (2) x = C(1+ cos…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: (In a + 12x y cos a + x*y cos x)dx + (8xy cos x + 2x"y sin x)dy = 0, 4 2 y(T) = 1/27 b. y da - a(a?…

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Q: The general solution of y"+ 16y=cost is: Select one: a. y = C,cos(4t)+ C,sin(4t) + 1 cost 15 b. y=…

A: Here I am attaching image so that you understand each and every step.

Q: Match the following guess solutions yp for the method of undetermined coefficients with the…

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Q: Integrate with respect to x: sin(3x) a b 2 cos(4x) cos (2r) (5) f e2x cos² () d 3 cos 3 sin(2a) — е…

A: We have to solve the following integral .

Q: If y= x2 sin 2x, then y = А) 2х cos 2x B 2x (sin 2x - x cos 2x) C 2x (sin 2x + x cos 2x) (D) 4x cos…

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Q: day Find y, of 2+ + 6y = 51 cos 3x. ... a.) y, = - cos 3x + 4 sin 3x b.) y, = cos 3x-4 sin 3x c.) y,…

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Q: What is the general solution of sin x sin ydx + cos xcosydy = 0 O tan x = O sin x O sin y + cos x +…

A: To solve the given differential equation.

Q: Find the general solution of (cos cos y +ycos x ) dx + (sin sin x – x sin sin y ) dy = 0

A: The given differential equation is incorrect and hence the correct differential equation is as…

Q: If z = 24 - 2x - 6y, x = cos(4t), and y = esint, then dz dt is equal to O-2 sin(4t) - 6esint cost O…

A: Since you have posted multiple problems we will answer first problem for you for remaining problem…

Q: 3. (sın 2y - 2x cos 2y) dx +( 2x cos 2y + 2xsın 2y)dy=Dd X = 2, Y = TT when

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Q: r5x V2 - cost dt dr 2/2 a) 5/2- cos 5r COs 2r b) 5/2 COs 2r 2/2 COS 5.r 2/2 cos 5r - COS 27 d) 2/2…

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Q: f cos(mx) cos(nx) dx is equal to {A} [sin(m + n) + sin(m − n)] dx {B} [sin(m + n) - sin(m - n)] dx A…

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Q: d²y 10. dx2 -- 3y = 2e2* +10 sin 3x given that y (0) = 2 and y'(0) 4 dx %3D 29 Ans. 12 e2x +[cos…

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Q: Following S sin(A) cos(B) dx = ; f sin(A + B) + sin(A – B), | what is the integral of f sin 5x cos…

A: We have to solve the following

Q: Integrate with respect to x: sin(3r) a b 2 cos(4x) cos (2r) (5) f e2x cos² () d 3 cos 3 sin(2a) — е…

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Q: 1. L(e** + e¬* + x²) S-4 s+1 s3 e3 2. L(sin 2x + e²x+3) : 2 + s2+4 s-2 Hint: e2x+3 = (e2x)(e³) %3D…

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Q: If it was f(x,y)=y cos(6xy) SO a² f Əy² 2² f Əy² a² f Əy² a² f Əy² = 36 x²y cos(6xy) + 12x sin(6xy)…

A: A detailed solution is given below.

Q: (sın 2y - 2x cos 2y) dx +( 2x coS 2y + 2xsın 2y)dy=d when x= 2, Y = T 3. COS %3D

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Q: Differential Equation Activity

A: To find the general solution of the given differential equation

Q: the initial value DE y' - ytanx = sinx, y(0) = 1 cos 2x 5-cos 2x %3D 4 sin x 5-cos 3x 5-cos 2x В) у…

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Q: If z = x2 – y2 and x = t cos 2r and y = r sin t , then a²z is (A) 2 cos?(2r) + 2r² cos²(t) – 2ry sin…

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Q: Show that an implicit solution of 2x sin?(y) dx - (x2 + 17) cos(y) dy = 0 is given by In(x? + 17) +…

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Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler or Runge - Kutta method, what is…

A: