following GDES by variation of param 29 js 28 • ý -2ý +y- ě sinx = e Ans: y= Ge +C2 xể - ễ sinx e sin • ý ý -4ý +uy =12 /x*

Q: 1) Evaluate the following line integral:S. (x? + y? +z?) ds where Cis parametrized b :r(t) = ti +…

A: Introduction: The function to be integrated is determined along a curve in the coordinate system for…

Q: The linear approximation at r 0 to sin(2r) is A+ Br where A is: and where B is:

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Q: Which of the following DEs is not homogeneous? (1) xy-y² = d dx (3) sin dx+ + In dy = (2) (x² –…

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Q: Find the position function of the particle moving along a line that satisfies the a(t)=4 sint-cos t,…

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Q: Given z = 64 sint+ 5 and y = 64 cos t + 4 da (i) dt dy (ii) dt dy (iii) dx || ||

A: Using derivatives of parametric function.

Q: Write the DE, e"y' + e2y= sin a in the general form. A. e dy + ydr = 0 sin r C. e dy+ (ey- sin a) dr…

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Q: nd die velocityi Tation, anmd spe particle With the given positIon fun r(t) = (4 cos(t), 3t, 4…

A: Derivative of position is called Velocity and derivative of velocity is called acceleration

Q: et w(x, y, 2) = x² + y² + 2² where z = sin(7t) , y = cos(6t), z = e". %3D dw dr dy dz by first…

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Q: y=6 In(cos(e7")). dy AeBt sinC (e7 dt Then %3D cosº (e7) where A = %3D %3D D = BCD

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Q: Consider the integral dx I = 3 x+2 The approximation of I using the two-point Gaussian quadrature…

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Q: Is the differential 2re sin ydr+e cos ydy exact? If yes, then the funetion f from which it is exact…

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Q: Solve the DE by Variation of Parameters (D³ + D² – 2D) y = 4e 2" cos a Cos r y (0) = 0.4, y' (0) =…

A: given (D3 + D2 − 2D)y = 4e−2x cosx The auxillary equation is m3 + m2 – 2m= 0 m(m2  + 2m - 2)=0…

Q: Calculate ôz/ðu and dz/ðv given the following functions: 2x – Y z = f(x, y) = x(u, v) = e²u cos 3v,…

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Q: ム)Find the solution f zhe intiol Volue Poblem Siven below by using Lapiece Tronsform the method.…

A: We have to use Laplace transform Method and basic formulae in Laplace we get general solution.

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

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Q: Evaluate the line integral (cos x + sin y) ds; C is the line segment from (0, 0) to (x, 67).

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Q: The solution of Laplace equation d'u = 0, where 0 < x < 3 dx? and 0 < y < 2 with boundary conditions…

A: Step:-1 Since we know for Laplace equation if step size h= k then ui, j=14ui+1, j + ui-1, j + ui,…

Q: plve the following second order (non-homogeneous). d²y dy 2y dx = sin2x dx2

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Q: show that the Punctionc Sinh t V3 and ye T5 Sinh t+ CoshE 13 taken together satisfy thediff erential…

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Q: Given the force field F = (2xze*z – 4, cos³z, x²e**z – 3ycos²z sin z) Solve for the work done by F…

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Q: Which of the following is/are linear equation/s of the first order? (2s e) ds = 2 (se - cos 2t) dt…

A: Topic- differential equations

Q: dy +w?y = 0. dt2 Verify that y(t) = c1 cos wt C2 sin wt is a solution of the DE:

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Q: Which of the following is not linear? a. 3. 2x + Vy? – Vz3 = 4 (sin T1/2)x1 + 4x2 = cos245 b.…

A: Which of the following is not linear? a 2x+y2-z33=4b sinπ2x1+4x2=cos245c 12x-y+πz=4d…

Q: You are given that z= ry- s2 + sint and y=t+s. where I= %3D %3D Select all statements below that are…

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Q: Write the DE, e"y' + e2y = sin z in the general form. A. e dy + ydr = 0 C. e dy+ (ey- sin a) dr 0…

A: topic - differential equations  option C

Q: If f(x, y) = 19e CoS I +7 cot y, then the total differential of fat (0.) is: 4 O df= 19 dr + 14 dy…

A: Let the function is f(x, y)=19e-xcos x+7cot y Total differential is defined as df=fx(x, y) dx+fy(x,…

Q: /1+x² + y² dS where S is the helicoid: r(u, v) = u cos(v)i+ u sin(v)j + vk, with 0 < u < 5,0 < v< 4n…

A: Let I = ∫∫S1+x2+y2dS and r(u,v)=u cos(v)i +u sin(v)j+vk We know that dS=ru×rv du dv Consider ru =…

Q: RT a P = V -b T²v(v+b) – b 1/2

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Q: Solve the DE by Variation of Parameters (D³ + D° = 2D) y = 4e¯= cos z -2x COs I y (0) = 0.4, y' (0)…

A: The differential equation is D3+D2-2Dy=4e-2xcos x with the initial condition y0=0.4, y'0=-0.4,…

Q: Q. find each line integral along the two given curves C, and C2. So(x + y) ds (a) C: x=1, y = 3t, 0…

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Q: Calculate (yz +r + y,rz+r+2, ry + 2yz + e²=) - dr, where C is given by r(t) = (t² cos(2nt) +t*, t² +…

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Q: • T/4 cos(0) f |/| f(x, y, z) dV = 9p sin(ø) cos(4) dp d0 dø, find f(x, y, z). E f(x, y, z) =|| ?

A: We have to given ∫∫∫Efx,y,zdV=∫0π2∫0π4∫0cosθ9ρ2sinϕcosϕdρ dθ dϕ Now the function which is to be…

Q: 2. Find the complex potential function f(z) = u + iv, given that 2u +3v = e*[cos(y) - sin (y)]. Also…

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Q: 2.Figure out the following = 2t2 +Int, t>0 dy. = cos(t – 1) c.f(z) =| -1|,9(z) =| 1.f'(1)?g/(0)? ?…

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Q: If f(r, y) = 22e cos z +2 cot y, then the total differential of f at (0, ) %3D is: O df = 22 da +4…

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Q: Express the given parametrization in the form y = f(x) by eliminating the parameter. x = 1/5…

A: Express the given parametrization in the form y = f(x) by eliminating the parameter.

Q: Ex: verifay u = e* cos y is a solution of laplace eqution

A: Solution:Given             u=ex cos yTo verify u is a solution of Laplace equation:i.e.,…

Q: dw at t 0 is 5? dt Let w = sin(zy+) where z = eat and y = In(at +1). What is the value of a if %3D O…

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Q: Exercise 5 Normal. , e-x² dx = \TT -00 Use 1? = (Se-x* dx)( S,e-y² dy) = L. Le-(x²+y²) dx dy = Sp2…

A: Find the valve of the integral

Q: Calculate dz/du and dz/dv given the following functions: 2x-y x + 3y' = f(x, y) = = Z = x(u, v) =…

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Q: Consider the 2nd order equation d²y + Sin dy + y? +y = 0. dt, Choose the right assertion A) the…

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Q: Let y= a,+a,t+ azt? + a3t³ + a4t* + agt5 + agt6 +...... be the solution of d?y ад dy +t- +y=tan-'t ;…

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Q: Which of the following is NOT a variable separable DE? A B C D sinydx + cosxdy=0 (x+y) dx-xydy=0…

A: From the given Differential equations, we have to find the differential equation that is NOT a…

Q: H.w1: evaluate fe* siny dx dy i) using the trapizodial rule in both direction, Ax= Ay = 0.1 ii)…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: An object with an initial position of x(0) = 5 has a velocity of v(t) = sin 2t. %3D %3D What is its…

A: Given query is to find the position of the object at π.

Q: Use Green's Theorem to evaluate the line integral. e cos(2y) dx - 2e* sin(2y) dy C: x2 + y? = a?

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Q: Q.01: Use Green's theorem to evaluate the line integral £ e2*sin2ydx + (e²*cos2y)dy, where C is the…

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Q: USE HOMOGENEOUS LINEAR HIGHER ORDER DE 4. y(4) + 50y(²) + 625y = 0 ANSWER: 4. y = (C₁ + C₂x) cos 5x…

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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.