sin z dz (z²–1) 2 where c = |Z – 1| =; valuate at oriented lockwise? (12 M)

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: Q2/ by using chain Rule to find dw at t = 1 if dt w = 2ye* – Inz ,x = In(t? + 1), y = tan 1t,z = et

A:

Q: Solve the boundary value problem described by PDE: u„ - c?u = 0, OSxS1,120 BCs: u(0, t) =u (1, t)=…

A: The general solution for the homogeneous wave equation satisfying…

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

A:

Q: Ex 21Eulers method dy-y= - y Xーツ ーメー

A: We have to use the Euler's Method to solve                           dydx=y'=x-yx+y, y0=1,…

Q: 28. Evaluate by Green's theorem (x - cosh y) dx + (y + sinx) dy, where C is the rectangle with…

A:

Q: (b) cos(x² + y²) dy dx where R is the region 9 < x² + y? < 49.

A:

Q: riable t. If 2sin (x)+4cos(y)=3a dy and dt 3, what is the val

A:

Q: 2s – 5t & y = 6s – 8t. %3D Let z(x, y) = x + 9y? where x = az дх ду да dy dz Calculate ds & and…

A: We use the chain rule

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.…

A:

Q: Əs' at (1) z = x²+ y², x= s+2t, y = 3st (2) z = sinxcosy, x s-t, y = s² +t³ %3D (3) z = e" tany, x =…

A:

Q: dw w=x +y, x-cos r, y-sin/ ise dt Irm

A:

Q: 3(1 + 2) - dy 2ty(y – 1) dt

A: The method to find the solution of the differential equation helps to find the required solution.…

Q: HW 0 1f y=tanx show thats y" = -2Siny Cosy %3D

A:

Q: (Xy,Z)%3Dex(cosy +sinz) fr?, fy =?

A:

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

A:

Q: = f (x, y) is differentiable and x=u cos v and y =u sin v. Show that z = Oz Oz 1 + ди + и

A: According to question given that z=f(x,y) is differentiable x=u cos(v), y=u sin(v)

Q: 4хy + 5y? xy +3x? in x and z by using the substitution y = xz dy = can be transformed into a…

A: We will use the substitution to try to transform the given differential equation into separable…

Q: The Bossel aquation of order one halt, f'y y -y-o, 10, + ty+ has two linearty independert selutiorm,…

A:

Q: 1 Evaluate dV, where E lies between the spheres x + y + z = 16 and + y? + z2 = 64 in the first…

A:

Q: dw Use an appropriate form of the chain rule to find dt 1 y = t, z = to w = 3 cos xy – sin xz3; t'…

A:

Q: How can I evaluate ∭x2 dV, where E lies between the spheres ρ = 1 and ρ = 3 and above the cone Φ =…

A:

Q: W= Pcxiy,Z) = In (x+y+z) ,x= cost, 2. %3D 2X = Cost, y- Sint and z= 4VE >use chain rule to Rind dw…

A:

Q: Q1:- dz at t=al4 at Calculate z = f(x, y) : 4x² + 3y?, x = x(t) = sin t, y = y(t) = cos t %3D

A:

Q: (a) Compute the average temperature of a wire in the shape of a helix c(t) = (cos(t), to, sin(t)), t…

A: To find- Compute the average temperature of the wire in the shape of a helix ct = cost, t10, sint, t…

Q: 6. C is the curve of intersection of the plane 4x + 5y+ z = 0 with the cylinder x2 + y? = 4 directed…

A:

Q: dy IS let y = (cos r)m " then de sin z

A:

Q: Numerically integrate y=x-X+4 from a-0 to b= 2 using single segment trapezoidal rule. O 12 0 8 0 6 O…

A:

Q: If z = x? + y?; x = t sin t , y = 2t cos t dz then dt at t = is

A:

Q: Given that y + x + cos(xy) = 0. Show that dy/dx = ysin(xy)-1 /1-xsin(xy)

A:

Q: 9. xy sin yz dV, where G is the rectangular box defined by the inequalities 0 <x< T, 0 < y< 1,0 < z…

A: Given information: The integral is ∬∫xysinyzdV and the region is bounded by the rectangular box…

Q: O from the equation z = In(x² + y²) + Zyy Show that zxx %3D

A:

Q: 4. (a) Use the trapezoidal rule to numerically integrate from a = 0 to b= 2 /(z)-0.2+25 +3r

A:

Q: Given z=3 In(t) and y=9t² then find dy de dy da %3D

A: We use parametric differentiation

Q: 4. Evaluate x² dV G where G is a solid that lies in the first octant bounded by x2 + y? = 3z and z =…

A: We have solid G in the first quadrant bounded by x2+y2=3z and z=3 equating the above two equations…

Q: 10 The double integral 2x dædy, where T is the triangle with vertices (0,0), (3,0) and (6,3), equals

A:

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 6 cos x – sin xy; Y = 8t %3D t' Enter…

A:

Q: A)lf y = sin¯¹ (3) prove Zyy + z = 0 B)Z = 1+ Ini, find [21.

A:

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: 14. Evaluate 4y dx +3ax dy, where C is the trapezoid with vertices (0,0), (2,0), (6,2) and (0,2).

A:

Q: 4. Find дw b. dz a. дх at the point (x, y, z) = (0, 1, T) if w = x² + y? + z? and y sin z + z sin x…

A:

Q: Given f(x,y,z) = 7xyz where x = sin(2t), y = cos(2t) and z = -1t. Find df/dt at t = -1. %3D Give…

A:

Q: Let f(x, y,z) = x? sin y+y e, where x = t+3,y = net-1 and z = In 2t. %3D at t = 1 is: df dt О 12п O…

A:

Q: (dy/dx -y =sin3x) is * O Homogeneous Non Homogeneous O Non of the above

A: The given differential equation is                                                dydx-y=sin3x…

Q: 8. Evaluate the line integral fx'dx + xe 'dy where C is the closed path along the triangle in the…

A:

Q: 3.4.6 Evaluate the line integral [sin y dx + (x- cos y) dy] taken in the anticlockwise sense, where…

A: Green's Theorem States that  Let C be the positively oriented, smooth, and simple closed curve in a…

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos x :- sin ry; y = 9t Enter the…

A:

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

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.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.