A 2.25 m -4 m- -e=90° µ=0.1 -3 m 3 m k= 200 N /m- 3 m -2 m-F1 m- 3 m -Inx -3 m- -3 m- F(x). boundary from x = 1 to x = 2 3 m B E E C. E

Q: 24. Evaluate x² dx + yz dy + (y²/2) dz along the line segment C joining (0, 0, 0) to (0, 3, 4).

A:

Q: 2: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G(x, y) = x³y² + y² sin…

A:

Q: ne if the curve (In t. t In t. 1) is tangent to the surface rz- uz? + cos Tu =1 at (0.0. 1).

A:

Q: Find the external in the isoperimetric problem of the extremum of subject to f(y² +xy'- :“)dx= 2,y…

A: Consider the functional  Iyx=∫x1x2Fx,y,y'dxwith the conditions yx1=y1 , yx2=y2and Iyx=∫x1x2Gx,y,y'dx…

Q: So lve the di fferential equation dy + y - ecos x = 0,0 s x s0.5, y (0) = 0 by (a) Milne's me thod…

A:

Q: Given =흙(1+ 들교 -볼 - 클시. dy 2 3 (1+ x – dx 2 What is the value of k such that y is parallel to the…

A: topic- slope of the curve

Q: M-2-Sin(X y) nd dm dt X = t. yclint Z=et-1

A: Differentiation

Q: A) The position of a particle P(x,y) at time t is given by: x= (2t +3) , y =+t.Find the distance it…

A:

Q: ) (4,0) ) (이14) ) (4,시) S. x* dy - 2y dx whare L is 2° J. circle arc x+y% =1, x >O X 70

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: Given that dy =0 dx when x=1 for the curve y=x³+ 3x2 – 9x +6 d?y Find dx- and hence find which of…

A:

Q: ula 0ニ こ0 2

A: Find solution using variable separation.

Q: dy When reduced to a linear DE of order one in z, the Bernoulli's equation +y = = 3x?y? becomes (1…

A:

Q: Which of the following gives the length of the curve y = Vx over the closed interval [1,4]? (A) - dx…

A: Explanation and solutions is given below....

Q: When the radius r of a sphere increases with time t, the change in area dA is dt Оа. 4 3 O b. dr 8n…

A: We will find the change in area with time as following.

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

A:

Q: a. Solve the boundary value problem d? y +7y = 0, with conditions y(0)=1 & y(37)=0. 2 dx?

A: first find its solution

Q: Given a+ yx = e¥ , what is 1-y dy dz 1+y dy 1+y dz 1+y el-I

A: Given equation is x+yx=ey We have to differentiate the given equation. To differentiate given…

Q: W3:- Estimate y(0.2),using Euler methe ere y': = -y?cosx „y(0)=1

A: Here we have to estimate y(0.2), using the Euler method with step size h=0.1 where,

Q: Ju こ0 二0 on 2) ne 「Xこo u la,e)=0

A:

Q: (d) S (1, y) = sin (2), (x, y) # (0,0) 0, (x, y) = (0,0) (e) , r + y # 0 7+y x² + y = 0 0, f (x, y)…

A: Limit of a function: A function f is said to tend to a limit l as a point x, y tends to the point…

Q: Solve the boundary value problem (D² + 9)y = sin² x given that y(0) = 0, y() =

A:

Q: 3. The length of the curve determined by the equations x =t and y=t from t=0 to t= 4 is a. b. 2[VF…

A:

Q: Find the solution to the boundary value problem: dy 6 + 5y = 0, y(0) = 7, y(1) = 9 dy df dt

A:

Q: If y is a function of x, then the equation (y - a)dx + 3ry dy = 0 is not linear + but both + and…

A:

Q: Evaluate Ic (2x - y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32) X

A:

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

A:

Q: = (b) ſ sin (7(x – 2y)²) dA, where T is the triangle bounded by x – 2y T 1, y = −3x and 5y = -x.

A:

Q: B) Find the distance traveled by the particle P (x.y) between t = 0 and t 4 if the position at time…

A:

Q: I don't understand why y= c3(cosay-cotay) when c4=cotay

A: Given that, Yy=c3cosay+c4sinayTo check: whether Yy=c3cosay-cotay  when  c4=-c3cotay

Q: y' + 4y = e^(4t) %3D

A:

Q: um,0) =)0 sn So

A:

Q: Find the temperature u (x, t) for the boundary-value problem ди 0 0 u(0, t) = 0, u(L, t) = 0, t> 0…

A: Given: ∂2u∂x2=∂u∂t ......(1) Let ux,t=X(x)T(t) ∂u∂x=TX' ⇒∂2u∂x2=TX''and ∂u∂t=XT' using in 1, we get…

Q: hich of the following is not variable separable? (А) 2ху dx + (х2 + 1) dy %3D0 A ye' dy - (e-y+…

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: Solve the given boundary-value problem. (If an answer does not exist, enter DNE.) y" - 2y' + 2y = 0,…

A: Given differential equation is a homogeneous equation with constant coefficient. We use auxiliary…

Q: (A) Evaluate" [(x² + y)dx + (x + 1) 1+ along the path ABCA shown in figure C(0,3) A(0,1) x=3sint…

A:

Q: Evaluate the line integral ( 9х + 5у)da + (х — у)dy along the curve C : x = 6 cos t, y = 12 sin t…

A:

Q: Find the Green's function for the boundary value problem d²y/dx? + µ°x = 0, y (0) = 0 = y (1). %3D

A: To find Green's function first we find two solutions of the differential equation using to given…

Q: Calculate the solution of Laplace's equation inside the circle of radius r = 1 with the following…

A: Given That : f(ϕ)=V00&lt;φ&lt;π0π&lt;ϕ&lt;2π where V0 is a constant  To Find : Solution of Laplace…

Q: Sketch the regions enclosed by the given curves y-4 cos(7x), y- 4 sin(14x), x -D, x-/14 0.05 0.10…

A: The solution of above question is written below.

Q: 1) Find the solution of the following equation: y"+ ly 0, with y (0) = 3 and'y (0) = 3 with A<0. Is…

A: Let λ=-a2&lt;0 Then, y"+λy=0 ⇒y"-a2y=0 Auxiliary equation is m2-a2=0 ⇒m=±a So, the general solution…

Q: S, (x + 2y) dx + x dy. C consists of line segments from (0. 0) to (2. 1) and from (2, 1) to (3, 0)

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: 46. f(x. y) dx dy

A: Let us consider the integral I=∫ab∫h(y)g(y)f(x,y)dxdy To draw the region of the integartion…

Q: If f=(3x?-3yz)i +(3y² – 3xz)j+(3z² – 3xy )K, then the value of the integral (f.dī along the curve x2…

A:

Q: dy x2 + y2 if dx Find at (x, y) = (5, 6) and z? dz dt = 9 and = 7. dt dt dz dt Additional Materials

A: To determine the derivative.