Use methed of Cardinates to Solve PDE du t 37gu = o (32² +81y -3y) for V 64) E R for Y te B with the condition ul-it,€) = 0 Vt e

Q: ®. *,(t)=l, tilt)=t, Xglt) =t² Let [oD. Use Gran-Schridlt on er thogonolize e, 2) process to

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Q: 8.Evaluate the triple Integral. Te by The paraboloid X=2yt + 2z? and the plane X=2. 7x dV, where E…

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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…

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Q: UseThe Culerwe method's Sove the: dy %3D xCi+メ)。 y(0)=3,h=0.2

A: This is a problem of Numerical Analysis.

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…

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Q: au a²U dt dx² Show that the local truncation error at the pint (ih,jh) of the Crank-Nikolson…

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Q: H.W p.564/ use Trapezoidal method and Simpsons' rule to evaluate. dx 1) So √1+x² n = 4 se as Ars

A: # as per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Wz bisects LXZY and X = LY. Which choice of method can be used to prove 4XWZ = AYWZ? O sS O AAA O…

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Q: 4) Solve the followingIVPusing LaplaceTransform. y′′−6y′+15y=2sin(3t)    ,y(0)=−1,y′(0)=−4

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

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Q: Consider The falloming Parumetric eguatin O54=?4V X Ct) Zsinct) +cos (t) Wing calulus , fund all the…

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Q: dr Consider the integral I- composite Trapezoidal rule with n-4 subintervals is: The approximation…

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Q: T 2 If fo)= J* +?dt, use the fundemental theorem of culculus part 1, to find f'cx) fixs=

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Q: Find dey -. The initil dx² condition Xo=0i y=10, %%=5&h=,by using yro1), given Runge -Kutta method…

A: Given second order differential equation is d2ydx2=y3                  (1) with initial condition…

Q: Evaluate the line integral/ (ax + 2y)dx +x dy, where C consists of the path C from (0,0) to (3,0),…

A: Consider the provided question, Hello. Since your question has multiple sub-parts, we will solve…

Q: The path integral v- dr, where v = (sin y, x - cos y) and C is the perimeter of the triangle formed…

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Q: The work done W,to stretch a spring from its natural length to an extension of b meters Is 6. given…

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Q: COS. dt, for alla at, for all r 58 1 dt 58. for |x| < 1 (1 – t4

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Q: 8- Solve ihe separation of variable MeRod satisfy %3D The condilion as tp0 as for x=0 and a =a T=メ…

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Q: auchy - Goursát heorem to show that dz = 0 %3D 22 + 5z + 6 Cia tho girelo Lel hoth diroction

A: In this question, concept of Cauchy Goursat Theorem is applied. Cauchy Goursat Theorem If a function…

Q: ) USE THE METHOD OF VARIATON OF PARAMCTERS TO SULVE THE GIVEN ODE 8" +y'= secx Sec'x %3D

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Q: Find thequahen. perpenditar to i fine -個 epe at OD pr Find tha liit ultpy cen gale (ro a) Po FO…

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Q: 4. Determine the c, and c2 so that the y(x) = c,e-* + cze8x + sinx that will satisfy the initial…

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Q: Find the temperature u (xjt). in a bar of Length t which is perfectly insulated everywhere including…

A: temperature distribution u(x,t), follow the partial differential equationdudt = d2udx2   ,…

Q: The value of the line integral | F(r).dr when C F(F) = [-y, -xy]and C is the upper half circle arc…

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Q: Using a suitable substitution, the integral T/4 9 (13+tan t)8 sec? t dt of

A: Given,          ∫0π4913+tant8sec2tdt

Q: Use the method of undeterminad Coefficiento to slve the initial valene proalem : yo +Qy'+5y=cin…

A: The given initial value problem is              y''+2y'+5y=e-tsin(2t)  , y(0)=1, y'(0)=0 We find the…

Q: 4)Solve the followingIVPusing LaplaceTransform y′′−10y′+9y=5t,y(0)=−1, y′(0)=2

A: The differential equation is given as y''-10y'+9y=5t Apply Laplace on both sides, we get…

Q: Find an interval where the IVP dy (In t) + y = cot t dt y(2) = 3 has a unique solution.

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Q: Solve the DE, dy =y²-a? E, = , using the homogeneous method. ry (a) Hint: Rewrite the RHS as 2 -…

A: dydx=y2-x2xy⇒dydx=y2xy-x2xy⇒dydx=yx-xy⇒dydx=yx-yx-1 Now put, y=vx⇒dydx=v+x·dvdx

Q: The integral JJI eV 4x2 + 4y² + 4z² dV = mt, where R is the solid hemisphere with x2 + y? + z² < 11…

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Q: 1 Evaluate dV, where E lines between the spheres a2 +3? + 22 = 1 and E 22 + y2 + z2 = 9 in the first…

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Q: The longest interval in which the 1.V.P y"+(tanx)y-xy = x, y(1) = 3, y'(1) =0 surlay has a solution…

A: Given differential equation is. y''+tanxy'-xy=x The initial condition as, y1=3,  y'1=0 On comparing…

Q: Using the approximation dy dy * Yn+1 - Y, and that dr 1, y = 2 dr h when r= 0. Then, y, = A h-2 h+2…

A: Use the approximation hdydxn≈yn+1-yn and that dydx=1, y=2 when x=0. Then y1=?

Q: Calculate the trapezoid approximation of 5dx using four subintervals. O T5 = 0.60 O T5 = 0.40 O T5 =…

A: The trapezoid approximation of the given integral is given below.

Q: A string of length 1m attached with two points. The deflection in the string is given by y" + Ay =…

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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: Solve the problem with Neumann oundary conditions, - Uxx = 0, x, t > 0 u(x, 0) = f(x) ux (0, t) = 0…

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Q: How to solve the ordinary differential equation using separation of variables?

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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: 3- Evaluate the below integral 3 2x Evaluate I = [ (x² + y)dydx . (Use 4 segments in each direction)…

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Q: Given that F) = (yet coso)+(ayé-xsing)5 is conservative on R? (a) Find Potential gGay) Por F. (b)…

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Q: Given that F(x, y, z)=sin x i+cos yj+ xzk. Evaluate , F.dr where C is given by r(t)={r',-f,t) :…

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Q: Consider the solid Q shown in the following figure 2.x + 3y + 3z = 6 S y? + x = 2 2 If S: 2x + 3y +…

A: The given surface is as follows: 2x+3y+3z=63z=6-2x-3yz=136-2x-3yz=2-23x-y The projection of the…

Q: Q1. Solve the follounig ordinary diflerential agethins, 2 ci) dy ;If yoo when x=0 = xe dx dy + Cot y…

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Q: Find Particular Sol. of  xsin2 ycosy y' + sin3y/ 1+lnx = 4 ; y(e)= π/2

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Q: The function U(x, y) satisfies the equation = -2, ax2 ' ay2 ду? at every point inside the square:…

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Q: The longest interval in which the I.V.P y" + (tanx)y-xy x, y(1) = 3, y'(1) = 0 surlay has a solution…

A: Given,  y''+tanx y'-xy=x It is of the form,  y''+p(x) y'+q(x) y=g(x)

Q: Find eauation of ny Perbola at o Ne tne foci Fz the and crankshafto f Fi Fz ny Perbola= Fi F

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