X+ xy B. Evaluafe the tripe in tagral S5* xy dydzdx,

Q: If  x2 + y2 = z2, find dy/dt when x = 3, y = 4, dx/dt = 6, and dz/dt = 2.  (Enter your answers as a…

A: Solution: the objective is to find dy/dt

Q: • Evaluate . 5y²dV where E is the reqion below x + 3y + 6z = 9 in the first octant. dxdydz dxdzdy…

A: Note:- As per our guidelines, we can answer the first three sub-parts of a problem. For the…

Q: Ex:@ Suppose thet the tallowing transformutioun Conneciãs the (x') and (xi) cordnate ار ک هأولاS…

A: Question: The transformation is T=x¯1=ex1+x2x¯2=ex1-x2 Calculate: (1) The jacobian matrix J and J-1…

Q: For the ODE dy = y² – 3y dt find a(yo) for Yo < 0 O 00 -V3 O V3

A: Answer

Q: EX. Use Euler's method (moditied) t appro y' = x+y for y C1) = 1 ; h =0.1,13XL2 Ư the açcuracy of E…

A: According to the given information it is required to approximate y'=x2+y for y(1)=1, h=0.1, 1≤x≤2

Q: Evaluate fSS, 5y²dV where E is the reqion below x + 3y + 6z = 9 in the first octant.

A: we need to evaluate the triple integration. For finding the solution first we will find the limits…

Q: Evaluate S, 5y²dV where E is the reqion below x + 3y + 6z = 9 in the first octant.

A: we need to evaluate the integration over the region using the triple integral. First we will find…

Q: woite x= psoduct x-6,62E; of dlementasy matsices. as a E2 3

A:

Q: The domain of the funsfon f(x) te 9) E2,21, or equivalenfly,t243 C) [4,00, 0r )(00,4),or…

A: This question can be solved by applying the concept of existence of function at various points on…

Q: 2. y(x-y²)dx + x(x++y²)dy = 0

A:

Q: Q2= A) for E= 2xĭ-3Y3+K %3D prove That divc curl È)=0 %3D

A:

Q: D Find the Valve of K So that the fallowing Where u= (XxXz) V= (YY) inner praduct in an.

A:

Q: For the ODE = y² – 3y dt .2 find w(yo) for yo < 0 3 V3 O-V3

A:

Q: Linerije he lien apantion: 1. yeation; nen- x* xy+ 3y sie the ryin *T/ テ

A: Solution: We have to linearize the equation z=x2+xy+3y2 within the region 2≤x≤3,  11≤y≤12 Let us…

Q: find the Solehion dy'= 4t + 2e

A: Given the differential equation :

Q: Q3: show that: S yi va -y dy =na² where a is a positive constatnt

A:

Q: Please answer in pen

A:

Q: -8 6. Evaluate the integral +y² dydx

A:

Q: Classify the following PDE 3xuxy + x²uyy + ux – u = 0 A) Parabolic B) Elliptic C) Hyperbolic D)…

A: We have to classify the following Partial Differential equation according to its type. 3xuxy + x2uyy…

Q: Show that y^3dx+3xy^2dy=0 is separable and exact

A:

Q: The evaluation of S V1 + tan2x dx is C In(V2) +1 In(vZ+1) C In(vZ-1) O-In(vZ+1)

A:

Q: Evaluate | CurlF nds F(x,v,z) = - yzi + xzj – xyk, and S is that part of the cylinder 4= x² + y²…

A: Given function is  Fx,y,z=yzi+xzj-xyk To evaluate ∬SCurlF·nds where S is the part of the cylinder…

Q: S dy 7 y2-8y+5

A:

Q: H.W: Evaluate the integral 3. -4y)dydx x*ydxdy 1 -1

A: ∫xndx=xn+1n+1

Q: Sy²el+2y®dy

A: Consider the indefinite integral ∫y2 e1+2y3 dy to evaluate the above indefinite integral, use the…

Q: -Skatch the reglén of Etyndtion , reversed the order of itegral and evaluade dx dy 7 | +

A: We have to sketch and after changing the order of integration evaluate it.

Q: Find an equatlon Of the ine Through G1,2); Perpendicular to me 2x+ 5yt 8=0 line

A:

Q: Assume w = ts³, 4ts) and (x,y) = 6xy of (х.у) - 4х Find as when t = s = 1 %3D

A: Given: From the given expression it is clear that 'f' is a function of 'x' and 'y', and 'x' and 'y'…

Q: [5] Use the Gaussian quadrature to approximate the integral 1 x²e¬*dx. (a) Choose n = (b) Choose n =…

A: As per instruction we are allowed to answer only two sub questions. The generalised Gaussian…

Q: Qs Findl the Fauier Ex pensian of Hhe funckian deld in a gula Parul by the weladons Sule Perial by…

A: To

Q: Q2) Is the ODE separable or non dy x² + 3y2 2ху

A:

Q: Eva 6 SSin'z osx dy

A: ∫undu=un+1n+1.     cos2x+sin2x = 1

Q: The auxiliary (charasteristic) equation of the DE x²y" + xy' + y = 0 is %3D

A: Euler-Cauchy type differential equation: Let a equation x2y''+y=0 ..(i) Put y=xm in the given…

Q: H.w, considev The SyoLem by and Gass Jorolan limnat 8x-23+3=25 メ+33-2るー12 uメー5y - 3)

A: we have to find the solution of the system by Gauss - Jordan method.

Q: (3) = 2 u + U, =D2 at ucx, t) fipdy ing the following initial condition : - -3X U(x,0) = 6e

A:

Q: becB.2. Evaluatte fhe vpperbound for R,(X) G0 for fulecosx

A:

Q: Given y = Va In æ , what is dy dr In z+2 In z+y7 dy dr dy dr In z-2 dy In z-I dr ||

A: Given,

Q: H.W. a PDE from the followi'ng- @u=f() Form メツ 0u=fcx?ー)

A:

Q: If z = e4x + y In(x), find zx and zy. Zx Zy %3D

A: 1) The given function is: z=e4x+ ln(x)

Q: = √ √ XY S: z = 9-x-y, first octant Evaluate xy ds.

A:

Q: F the generl solution of y=2 by reduing itto a frust order ODE the depandant vaiable the indepandurt…

A: y''=2 integrate both sides with respect to x y'=2t +c1 c1 is the integration constant Integrate on…

Q: Findd Fhie boundled by Ahe Cureo area 2. X= 3J-y' and x+Y=3 ーレ

A:

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: Find a general solution to (x' +xy')y' = y implict form F(x, y)= C : Give an

A:

Q: IF Y = u²-1 u²+1 Find dy np

A: Given,  y=u2-1u2+1

Q: Evaluate JI (x* +y)dxcdy on B region using the transformation 1= xy and v= x²- y xy= 2 = شر هړ. B و…

A:

Q: 2 I| ysin(xy)dydx Н.W.

A:

Q: D Reduce the Q.F 22,xz t 22,X3 2ズュズ3 weag ayf of oothogonal toans fermation by an Ans: y+92-295

A:

Q: l? sc tue suell metuozd to fired tue voune of te Solid genented the by rerolning the plene rgim…

A: