II. r*yz dxdydz K = {(x. v. z) : 0

Q: H.W3:- Estimate y(0.2) ,using Euler method with step size h=0.1 where y':= -y?cosx „y(0)=1

A:

Q: Let I = L,x? cos(x + 1) dx. The approximation of I using the two-point Gaussian quadrature %3D…

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: Find the length L of the curve R(t) = e* cos(3t) i + e* sin(3t) j + 3e*k over the interval [1, 5]. L…

A: given: Rt=etcos3ti+etsin3tj+3etk interval 1,5

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: а. y' +y tanx %3D sесх + сosx b. 1 -/dx+x?dy)=0 (x² - y?) C. yy' – 2y? = e* С. d. 1 -(хdy - ydx)3D0…

A:

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: dz evaluated at dt If z=tan In with x=sec t and y=eª. Then the value of t= 0 is equal to ...…

A: Chain Rule Let us consider the function z=f(x,y) where, x=g(t) and y=h(t) Differentiate the function…

Q: 2. Find the length of the curve 0<t< 2n. r(t) e'i + e' sin 2tj + e' cos 2tk,

A: From the given problem :   rt=eti+etsin2tj+etcos2tk   So,   x=et, y=etsin2t , z=etcos2t .   As we…

Q: If z=x+ iy=r(cos(0) + isin(@)) then |:|=/x? +y² =rO arc z=0 Z=rO

A: By definition of modulus u got |z|=r

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

A:

Q: Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS. xcos2y dx + tany dy = 0

A:

Q: (a) Determine the appropriate Green's function by using the method of variation of parameters for…

A: Green's Function: The Green’s function approach is particularly better to solve boundary-value…

Q: z= cos y Using the substitutions the DE (3cos y - 5x) dx – 2x?tan y dy=0 reduces to dz= - sin y dy

A:

Q: dz evaluated at dt 4x If z=tan In with x=sec t and y=e". Then the value of y t= 0 is equal to ...…

A: Given,             z=tanln4x2y with x=sect and y=e2t.To find : The value of dzdt at t=0.

Q: 4. If u = xy + y²z³, where x = rset, y = rs²e-t and z = r²s sint, find the value of du/ds and au/ar…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

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: Find the length L of the curve R(t) = e" cos(2t) i + e* sin(2t) j+2e"k over the interval [1, 4]. L =

A:

Q: (4) Evaluate sin(yz)dr+xz cos(yz)dy+ry cos(yz)dz, where C is any curve joining the point (0, 0,0) to…

A:

Q: H.W3:- Estimate y(0.2) ,using Euler method with step size h=0.1 where y':= -y°cosx „y(0)=1

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 particle moves in the xy-plane in such a way that its path is defined by x = e^t cos t and y = e^t…

A: Given that, x = e^t cos t y = e^t sin 2t Differentiating x with respect to t we get, dx/dt = e^t cos…

Q: 4. Given YZ tangent to oJ at point Y and m<WYZ = 104, %3D what is the measure of WXY?

A:

Q: where t is a non-zero parameter. Show that dx 28 Given that x=z and y==. 1+r Hence find its value at…

A:

Q: 6.(6 pts) Evaluate the line integral / (x+ y + 2) ds along the curve C given by r(t) = (sin t, cos…

A:

Q: 1.Evaluate S. (x² + y² + x²)-²ds where C is the helix x = cost, y = sint, z = 1 for 0 < t ST

A: The length dS is: ds=dtdxdt2+dydt2+dzdt2=dt-sint2+cost2+02=dt

Q: B. (y + e*seny)x + (x + e*cosy)dy = 0

A: The differential equation is given as  y+exsinydx+x+excosydy=0 Compare it with Mdx+Ndy=0 to obtain…

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) Find the length L of the curve y = x + cos x, 0<x <T/2 Use any one of the following formulas 2…

A:

Q: 4. What is the form of y, given (D² + 9)y = x + tanx? p = v¼sinx + v2cosx Yp = vịsin3x + vzcos3x Yp…

A: Given differential equation is of second order differential equation The general solution of DE is…

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: Find the particular solution with the given boundary condition. e*e°dx – e-2y dy = 0; where y = 0…

A:

Q: 3- Approximate xe* dx using h = 0.25. Use a. Composite Trapezoidal rule. b. Composite Simpson's…

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: T T 4. The region bounded by y = cos(x) and the x-axis between - 2 2 5. The region bounded by y = x…

A:

Q: (b) Given that = 3 in steps of 0.2, given that y = 4 at r = 2. dy = x+Vy. Use Euler's Modified…

A: Given y'=x+yy(2)=4   , y(3)=?       h=0.2  modiefied euler method is yn+1=yn+hfxn+h2 , yn+h2f(xn…

Q: What is the general solution of (2ry – tan y) dx + (x² – rsecy) dy = 0 ? %3D atany 222y 12 sec2 y =…

A:

Q: - Find the aera under the curve y = cosx Form x = 0 to x = -fx sec² (ax² )dx a#0

A:

Q: Find the aera under the curve y = cosx fx sec²(ax² )dx a #0 Form x = 0 to x = 7/

A:

Q: dy If y = f(x) is solution of dx? = 0 with the dy boundary conditions y = 5 at x = 0, and at x = 10,…

A:

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: 1) The Arc Length of the curve f(x) = coshx, 0≤x≤ In3 is: d. 312 12 3 C. b. 2²/2 0.33 lorod by…

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: The linear approximation at I = 0 to sin(3r) is A + Br where A is: and where B is:

A:

Q: Solve the DE shown below, with boundary condition y(1) = 1. (1 Point) %3D xdy - (4y + x')dx 0

A: GIVEN EQUATION IS LINEAR DIFFERENTIAL EQUATION.

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

A: Given:  position of particle is P(x,y) : x= 1/3(2t+3)^(3/2) y= t^2/2 +t

Q: 2²y ds, C:x = cos t, y = sin t, z = t, 0 < t < a/2

A:

Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = . %3D

A: Explanation of the solution is given below...