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Q: Which of the following differential forms are exact? (y² – t²) dt + (2ty – y) dy O ye' dt – e' dy O…

A: To find  Which of the given differential equations are exact.

Q: Consider the slope field shown. (a) For the solution that satisfies y(0) = 0, sketch the solution…

A: Given, the slope field:

Q: dz dt Consider x = cos t, y = sint and z = x2 +y². Then ulan ||

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Q: Transform the equation rydx – (z+2) dy = 0 into the form of a %3D variable separable f(z) dz + g(y)…

A: Here, the given differntial equation is: xy dx-(x+2)dy=0...(1) To write the eqaution in form of f(x)…

Q: Q7 Show that CX,y) =e is Condinuous at co,0)

A: The given function is:  fx,y=e-x2+y2 The given point is 0,0

Q: Let f(2) = z e 2 #0. z # What type of singularity does f(2) have at z 0? (Justify.) What is the…

A: The singularity of the function f (z) have at z = 0  .     Find the Taylor series expansion of z5…

Q: Let F(x, y) = (4ye™Y – 3x², 4.xe™Y – sin y). - a. Find a potential function of F. b. Find |F. dR…

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Q: Consider 6x (1+x²)² 2(x+y) (1+x²)² + 2y ý = Using the function V(x, y) = 12 + y² show that the…

A: What is Lyapunov Stability Theorem: Lyapunov stability theorem says that if a function is positive…

Q: 3. For all a? + y + 2? > 0, verify that the velocity potential 1 $(r, y, z) = Vr? + y² + z2 is a…

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Q: If u = x? + y? + z?, where x = e2t, y = e2t cos (3t), z = e2t sin (3t), %3D du at t= 0 is dt then

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Q: Consider the DE dx + kx – la? = 0, dt - where k, l e R+. Use a suitable substitution to transform…

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Q: Evaluate f(x + 2y)dx + (y – 2x)dy around the ellipse C defined by x = 4 cos 0, y = 3 sin 0,0 < 0 <…

A: Given the Integral : ∮c(x+2y)dx-(y-2x)dy ⇒Let I=∫C(x+2y,y-2x).(dx,dy) , x=4cosθ and y=3sinθ…

Q: Let w(z, y, 2) = x² + y² + z² where z = sin(7t) , y = cos(7t), z = e'. dz dy dw by first finding dt…

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Q: Use Green's Theorem to evaluate the line integral |(y - x)dx + (2x – y)dy for the given path. C: x =…

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Q: (b) 6xy dV, where E lies under the plane z=1+x+y and above the region in the xy-plane bounded by the…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: dw 3) Find dt if w 5 cos(xy) – sin(xy), x =,y = t, z = t3 at at 4) Let t =,u = x² - y? ,v = 4xy³.…

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Q: Show F(x, y) = (2xy³ + 8)i + (3æ²y² + 2e2")j is conservative by finding a potential function f for…

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Q: Let w = x2e2y cos 3z. Find the value of dw/ dt at the point (1, ln 2, 0) on the curve x = cos t, y =…

A: Given: w=x2e2ycos3z x=cost y=lnt+2 Putting x, y and z in w, we get…

Q: Let w = x^2e^2y cos 3z. Find the value of dw/ dt at the point (1, ln 2, 0) on the curve x = cos t, y…

A: Given  By chain rule of differentiation , we have

Q: 1. Give an equation of the tangent plane to the surface z = In(4y – x) at the point (3,1,0). 2. Use…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: (2) Use the transformaiton u = xy, v = x² – y? to find JJ (æ* – y*)e*³ dA where R is the region in…

A: Given: The region bounded by the hyperbola xy=1 &amp;3, x2-y2=3 &amp;4 Where u=xy and v=x2-y2

Q: Compute f cos(Tæ) dæ + 10xy dy, where y is a part of parabola y = 3x? from the point (0,0) to the…

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Q: Given F = (2xze*²z – 4, cos z, x²e*z – 3ycos?z sin z) 1. You are to show that the line integral S.…

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Q: dz at t = dt if z = f(x, y) = x² – 3xy+ 2y², x = x(t) = 3 sin 2t, y = y(t) = 4 cos 2t. Use chain…

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Q: Compute I = (2x²132²y+ 4xy)ax +(x'+2x²-y') dy+zdz along The curve C C4U Cz UG given in the figure…

A: Given To compute I=∫C2x3+3x2y+4xy.dx+x3+2x2-y2dy+zdz along the curve C=C1∪C2∪C3 given in the figure.

Q: Use Green's Theorem to evaluate the line integral (y - x)dx + (2x – y)dy for the given path. C: x =…

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Q: Let w=x² +3y² + 2z² where x=rcos, y=rsin 0,z=5t find dw dw ar' at

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Q: Let oce) = Jñ e %3D dt, xe R X- is sloww that e li) show that the function y = o)e* satirfies the…

A: The function is σx=1π∫-xxe-t2dt. To show: ∫abe-t2dt=π2σb-σa. Proof: ∫-xxe-t2dt=σxπAs e-t2 is even,…

Q: dy 3 4-1+2у, dt (0) = 1

A: Given dydt=4-t+2y   ; y(0)=1  with h=0.1

Q: Consider the 2nd order equation 2²y+ Sin dy y² +y = Choose the ight assertion A) the linearized…

A: consider the 2nd order equation d2ydx2+sindydt+y2+y=0 this is a non linear homogenous differential…

Q: Determine the linearity and solve for the general solution to the given DE dx = ecos y dy х cot y

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Q: Find dw/dt at t 1 if w xe + ysinz - cosz, r ! = 2/t, y = t – 1 and z = nt.

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Q: 1. Show that the problem may be formulated in terms of the velocity potential (r, 0) satisfying r dr…

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Q: Compute the plane tangent to the graphs at the indicated points using the given functions. (Let z be…

A: Note : As per the authoring guidelines, when multiple subparts are posted, only first 3 subparts or…

Q: Let F(x, y) = (4ye"y – 3.x², 4.xe™Y – sin y). a. Find a potential function of F. b. Find | F. dR…

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Q: Assuming that the equations define y as a differentiablefunction of x, use Theorem 8 to find the…

A: Given:           x3−2y2+xy=0,     (1,1)

Q: Q2) A) Verify that wry wyx for w x sin y +y sin x + xy. %3D B) Show that f(x, y) = e-2y cos 2x…

A: A) given that w=x siny+ y sinx+xy               ...i show that- wxy=wyx differentiate equation (i)…

Q: Use Green's Theorem to evaluate the line integral (y - x)dx + (2x - y)dy for the given path. C: x =…

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Q: . The uejveciion of a beam is governed by the equation d'y + 81y = 0 (x) dx %3D where o(x) is given…

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Q: Let z2=2+4i | [4 Im (2) +2 Re (2)] dz € = ž1=0 where C the parabola y = x² defined from z1 to z2 ·…

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Q: Q2) A) Verify that wry Wyx for w x sin y +y sin x + xy. s) %3D B) Show that f(x, y) = e-y cos 2x…

A: We have to verify that the equations satisfy the given conditions.

Q: If f(x, y) = 22e¯ª cos x + 4 cot y, then the (0, is total differential of f at - O df = 22 dæ + 8 dy…

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Q: Al/ compute 6(4+ ec©*) dx + (siny + 3x?)dy cosx Where c is closed bounded region lying in the first…

A: Given (A) The given integral is ∮4+ecosxdx+siny+3x2dy and the region lies in between x2+y2=4 and…

Q: 4x Estimate the error in the quadratic approximation of f(x,y) = e sin y at the origin over the…

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Q: (も2-164 460) (7) 167 t60) dy dt =y y (8)- ) Flad as a Function of t rntenal ou what He solution and…

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Q: if f(x,y) =x2y÷x+y and y(t)=  (x(t),y(t)) is parametrized curve in domain of f with y(0)=(2,-1) and…

A: The first step in solving the problem is to obtain the parametric equation. The initial values can…

Q: If a and ß are positive constants, show that the particular solution of dy %3D У (В — ау) dt that…

A: Given that dydt=yβ-αy and y=y0 at t=0 We have to find the solution of the above equation.

Q: Determine the solution of y dt + (2yt + I) dy -Ogiven that given that y (-1) = Q

A: 2. We need to determine the solution of the differential…

Q: the ( gmplicit valne ) Find differenciation of az at the given poin t. Sin (y)+ sin(yn) + Sin (z+X)…

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Q: find the general solution of the dipperential ation given below. y+ 2xy -xe-r?

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