F(x, y, z) = (6x° sin(y) + cos(18z), xº cos(y), – 18x sin(18z) + 6z°)

Q: (2y cosx + sin“ x)dx = sin x dy ,when x =",y = 1 5y= 1 %3D X 2

A: 2ycosx+sin4xdx=sinxdy,   x=π2,   y=1:A first order linear ODE has the form of y'x+pxy=qxLet y be the…

Q: Find the solution. (y -x + xy cotx) dx+ x dy = 0 A xy tanx ccosy +secx - xcosx B xy cosy = c + sinx…

A:

Q: y'sin = y cos a is solvable by?

A: given equation y' sinπx = y cosπx is solvable by separation of variables

Q: x' + 2x + y =sin (t) y' – 4x – 2y = cos(t) x(0) = 0, y(0) = 1.

A:

Q: (a) z = x2 + y² + xy, x = sin t, y = e'. (b) z = x2 + y², x = cos t + sin t, y = cost – sin t. %3D

A:

Q: Find the solution. (y - x- xy cotx) dx + x dy = 0 A) xy sinx = c + sinx - xcosx B) xy cosy = c+ sinx…

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Q: Find Fxx and Fxyz of: XX хуz y2+Cos (xz) f (x, y, z) : 2 Siny

A:

Q: b. Find for each system. dx x = – sin(3t) х— —1 + 2 cos t х 3D 4 cos y = cos(3t) y = 4 + 2 sint y =…

A:

Q: Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); fi-) U =

A: we can solve this as follows:

Q: Obtain the general solution using separation of variables x cos² y dx + tan y dy= 0

A: Given differential equation is: x cos2y dx+tany dy=0 Apply variable separable: tanycos2ydy=-xdx…

Q: The integrating factor of the LDE y'=x-2ycotx is A B с D sin²x sec²x csc²x cos²x

A:

Q: For the relation siny – y² =x²y– x+x , is dx 3x²y+1 А. cos y – 2y –x T – 1 3x² + 2y – cos y cos y –…

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Q: Evaluate: y +y = - cos X COSX A. y = 0, sinx + Ca cosx + x sin x 8. C, COSX + Ca casx t x cas X C. y…

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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: If Z= x³ +y* +(x sin y) + (y cos x), Find (Zxx+ Zyy=?)

A:

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sec-1 (x + yz)

A: Given that f(x, y, z)=sec-1(x+yz)

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sinh (xy - z2)

A:

Q: Find the solution of Uxy - x²y = 0, Uy (0, y) = y², u(x, 1) = cos(x)

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Q: uxx+uyy=0; u1(x,y)=cos x cosh y, u2(x,y)=ln(x2+y2)

A: Given:

Q: Solve the DE sinx siny dx + cosx cosy dy = 0 by separation of variables. A cosx siny = c B sinx cosy…

A:

Q: Solve the DE sinx siny dx + cosx cosy dy = 0 by separation of variables. cos y A sin x B sinx cosy =…

A:

Q: Find F′(x).

A: Given- Fx=∫02xcost4 dt To find- F'x Concept Used- The Leibnitz's theorem as  ddx∫gxhxft…

Q: В. Find dz/əx , əz/əy at the point (1,1,1) if x³ + z² + ye*z + xz cos y = 0 .

A:

Q: (2y cosx + sin* x)dx sin x dy, when x = y = =,y= 1

A: Given - 2ycosx + sin3xdx = sinx dy , when x = π2, y = 1 To find - Solve the following differential…

Q: dx1 2.x1 + x2 + x3 + sin(t) dt dx2 = -x2 – 2x3 – 2 cos(t) dt dx3 2.x2 + 3x3 dt

A: According to the given information, it is required to find the general solution.

Q: Find fa, fus and fz. f (x, y, z) = (5z)) 3z In (x*y cos

A:

Q: -y cos xy - 4x) dx + (- x cos xy + 2y) dy o 1. = 0 2x+3y Zar+3y 2.

A: Proceed as shown below...

Q: Find the solution. (y - x+ xy cotx) dx + x dy = 0 xy cosy = c+ sinx - x secx B) x siny = cx+ sinx -…

A: The given differential equation is y-x+xy cot xdx +xdy=0. The integrating factor of the linear…

Q: Find fa, fy, and fz. f(z, y, 2) = z In (a*y cos(52)) z In (a*y* cos(52)) fr = fy = f2 =

A: First order Partial differentials

Q: Find the particular solution of dy - 2y = x³ sin 4x, y(1) = 2. dx %3D -

A: Using method of Linear Differential Equation.

Q: 12) dy dx - = x cos (6x²), y(0) = 7 A) y == sin (u) B) y = sin(6x2) + 12 C) y = sin (6x²) + D) y -…

A: In the question we have to solve the differential equation. Bartleby's guidelines: Please post…

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: y² cos x - 3x3y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e x² - 1) dy = ((1 + x)2 -…

A:

Q: i. y = x-% % -4Vx ii. y = x+Inx+ sin(3x) iii. y = x° cOS X y = x° cos x

A: Use product rule of differentiation

Q: Find fr, fy, and fz. f (x, y, 2) = z In(x*y³ cos(52)) 4.3 fa = fy = fz =

A:

Q: The distance between two moving objects whose positions are given by ( x₁, y₁ ) and ( x₂, y₂ ) is…

A:

Q: Find the linear approximation to h(y)=sin(y+1) at y=0. Use the linear approximation to approximate…

A: Linear measurement is one-dimensional. A linear differential equation is an equation where the…

Q: dy at x=0. dx If y = (3x² + 4x + 5)(e* – cos 2x), then find %3D -

A:

Q: X Cos 9TTX² dx 2. 2. V= dTx²

A:

Q: cos y f(x, у, z) -D xz2 XZ

A:

Q: Verify the linear approximation at ( 0, 0) for e^x cos(xy)

A:

Q: Find dz/ðx , dz/ðy at the point (1,1,1) if x³ + z² + ye + xz cos y = 0

A:

Q: •ý -2ý +y= ě sinx %3D Ans: y=ě +2xě - ě sinx • ý -uý ruy = 12 /* %3D e 2X 2 ZX .2 +C2 X e + 20

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: * sin(Iny)dy is equal to y A -cos(ny) + C B none of these cos(Iny) + C y D cos((ny) + C cos(Iny) + C…

A: A standard integral in some cases can be converted to a standard integral with an appropriate…

Q: (у — сos-x)dx + cos x dy %3D 0

A: The given equation is y-cos2xdx+cosx dy=0 rewrite it as y-cos2x+cosx…

Q: Find fa, fy, and fz. f(x, y, z) = 3z ln (x³y³ cos(2z)) fx= fy= f₂ = =

A:

Q: x = u cos 0 – v sin 0, y = u sin 0 + v cos 0 -

A: Given,

Q: F(x, y, z) = (xy — 2², 2x+cos(yz), 2y² - sinz)

A:

Q: 1 COS Z dz, C : |2| = 3z Integrate counterclockwise 9. COS Z dz 3z

A: We have to find Given Complex integral using Cauchy Residue Theorem.