The general solution for uz + Uyy = 0, %3D u(r,0) = 1, u(z, 1) = 0, u(0, y) = 0, u(1, y) = 0 is O Elen sin(nz) + bn cos(-nz)] sin(ny) O Elan sin(naz) + bn cos(-nAT)| sin(nny) OElen sin(nxz) + bn cos(-nA2)| sin(nny) Olene + bne sin(nay) O n sin(ny) + bn cos(-ny)| sin(na) OE eze™ + bye sin(nz) 01. c be sin(ny) sin(nar)

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: If y = 12y sin(4z) – 12z sin(4y), then (z, y) = 6y? sin(4z) + 3z cos(4y) + h(x) O (z, y) = 6y²…

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Q: 1 y = e*(C, cos2x + C2sin2x) –xe*sin2x a. 2 b. y = e*(C, cos2x + C2sin2x) +xe*sin2x 1 y = e*(C,…

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Q: Consider the following IVP: у" +у'%3D-сos x;B у(0) %3D а, у(0) -b Find the general solution. A y (x)…

A: Solution of the differential equation

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: 2. Show that u(x, t) = cos(x – ct) is a solution of Ut + cuz = (0

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Q: Differentiate y = In (sin + cos ) cos -sin 2r Va(sin a + cos V") sin E + cos E 2r V(sin a + cos a)…

A: we will apply, chain rule: ddxf(g(x))=ddg(x)(f(g(x)))×ddx(g(x)) Sum rule:…

Q: Find where z = sin (x²) cos (y) COS © 6.x sin (x²) cos (y²) COS 2.x sin (2²) 2x cos 2.x sin (x²) cos…

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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: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sin-1 (xyz)

A: Given that f(x,y,z)=sin-1(xyz)

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work…

A: Evaluate ∫2x4x2-1dx          ...(1)

Q: t, 01 1 a.) f(t) [m (sh w + (cos w - 1)] cos wt + [[ -[sin sin OLL - cos w + sh w]]sin wet dw - 1…

A: Given the function is ft=t0<t<10t<0, t>1

Q: 21. Integrate x cos(2x² + 7)dx. sin (2x²+7) 4(x²+7) B. sin(2x²+7)+c A. +C C. D. 4 4 sin(2x² +7)+c…

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Q: 1) F(x, y, 2) = 3xyi + 2yz j+ 7xz k. 3) F(x, y, z) = 6 e" senyi + 2e* cos yj + 9z k. 5) F(x, y, z) =…

A: We will find out the required value .

Q: х. у 2) w=¨+2,x= cos“(t), y = sin°(1), z =-, at t = 3 Z Z t

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Q: 6. If V(x, y) = xsin x cos y + y² then, F-VV and it is equal to A. -ily sinx cos y sinx cos y]…

A: We can solve using divergence formula

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: 17. (D4 + 2Dz + 1)y = 5 – 3x² a. y = (C1 + C2x) cos x + (C3 + C4) sin x – 3x² + 17 b.y = (C, + Czx)…

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Q: 2 tan(4x-1)-3 cos²(4x-1) If we let u = 4x – 1 for the S dx, what will be the resulting integrand?…

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Q: Suppose we want to show a classmate the basics of how to integrate with the u-substitution…

A: It is basic of u - substitution.

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: + 9y = 9 sin 3x (Let y p = Ax sin 3x + Bx cos 3x.) y = C1 sin 3x + C 2 cos 3x - x sin 3x + cos 3x y…

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Q: The area of the region inside r = 2+ cos 0 and outside r = 4 – 3 cos 0 is given by | ((2+ cos 0)² –…

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Q: If  f(x,y,z)=ln(x2y+sin2(x+y))+227x228y2z229,  then    ∂4f ∂x2∂y∂z at (1,1,1)  is equal to

A: See the attachment.

Q: Differentiate y= sin'x- cos³x CO A. 3sin x cos x (sinx - cos x) COS B 3sio x cos x (sinx + cos x) C.…

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Q: is If u = x², v = sin (y) and w = e-3 then the value ofuv.w) a(xyz) %3D ans. -6x. cos(y) e-3=x.…

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Q: The general solution of y" + 16y3 cost is: Select one: a. y= C, cos(4t) + C2 sin(4t) + 1 -tcost 15 O…

A: Using Solution of Linear Differential Equation

Q: he Solve the y)-Sy'(x)+8y(x)-4y(x)-xcos(x) equation y,0)-cos(x)+xsin(x)- 41 19 sin(x)+ cos(x)…

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Q: Solve the problem: u – kuxx = e-t sin x , 0 0; satisfying the conditions u(0,t) = 2n, u(t, t) = 4n,…

A: Let the transformation ux,t=vx,t+Ax+B ...............(1)uxx=vxxut=vtthe problem ut-Kuxx=e-t sinx…

Q: Show that y1(t) = cos(3t) and y2(t) = sin(3t) are linearly independent for all t

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Q: sin COS dx V 32 COS 35 5cos² + C O 32 COS 32 + 4 COS 4 口 32 cosS Ssin+2-c cos () + c 35 4 4 32 CoS 7…

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Q: y sin 2x + cos 2y = ax Find y' a – y cos 2x y% = sin 2x – sin 2y а - 2у сos 2x y sin 2x – 2 sin 2y…

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Q: Find the solution of the heat conduction problem. 100uxx = ut,   0 0 u(0, t) = 0,   u(1, t) = 0,…

A: The solution of the heat problem is given by u(x,t)=∑k=1∞  aksinkπxle-α2π2k2tl2   where ak=2l∫0l…

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: az Use an appropriate form of the chain rule to find dt 1 z = 2 cos x sin xy; y = 5t t Enter the…

A: z=2 cos x-sin xy ; x=1t; y=5t   see z is a function of x and y ,where x and y are functions of t so…

Q: Use Cramer's rule to solve for x' and y' in terms of x and y. x = x' cos 0 – y' sin 0 y = x' sin 0 +…

A: Solution is given as below:

Q: 36. Sin(xy) + cos(yz) = 1. Compute z and az at P = (2, п/12,4). дх ду

A: Let us consider the given function z=f(x,y) The partial derivative of the function is obtained as…

Q: In Exercises 9-20, use the Chain Rule to calculate - f(r(t)) at the value dt of t given.

A: NOTE : As per Bartleby guidelines, incase of multiple questions only one will be answered. Please…

Q: 17. (D+ + 2Dz + 1)y = 5– 3x2 a. y = (C, + Czx) cos x + (C3 + C4) sin x – 3x2 + 17 b.y = (C1 + Czx)…

A: As per the company's guidelines we are supposed to solve first question for you, kindly repost other…

Q: A Jsin(3x)cos(4x)dx = [ sin(7x) – sin(x). A dx 2 * cos(x) – cos(7x) ® Ssin(3x)sin(4x)dx= [co c) All…

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Q: Find y, of 2 -3+2y 6 cos x+9 sin x dx ... a.) y, = 3 cos x+ 2 sin x b.) y, = 3 coS x- 2 sin x c.) y,…

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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. dz (1² + 5)² 2. COs z dz 3. sin 3r cos 5z de

A: Given: I1=∫x3x2+52dx, I2=∫excosxdx, I3=∫sin3xcos5xdx

Q: 3. f(x,y)= In(x cos y)-cos (In3y)+

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Q: 16) fx*«5 - 1)³ dx, u = x5 – 1 D) x30 - 1 +C 30 17) V9 - s4 S d, u-9-4 A) -45V9 - s4 + C -2 B) + C…

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Q: Solve the exact DE (2xy³ + cosx tan y +2 sin x)dx + (3x²y² +sin x sec² y-3 csc y cot y)dy = 0 (1)…

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Q: fip Ify r' sin I, dx a)3x²+ cos x 3. O b) 3x sin x + x° cOS I O cos x 3x sin x + x³ COS 2 Od 13…

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Q: What is the general solution of (r + sin 0 cos 8) dr + r (sin 0 + cos 0) d0 = 0 ? %3D rsind rcose =…

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Q: 44. First verify by substitution that y (x) =x=1/2 cosx is one solution (for x > 0) of Bessel's…

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

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.