A. Classify each of the following equations as to order and degree. Order | Degree 1) у" - 5ху' e* + 1 2) ty" +t?y' – (sin t)/y = t² – t + 1 d?t dt + st ds 5 3) s2. = S ds? (d+b + 7 dp*, 4) (db\10 5 + b' – b5 = p \dp/ d²y 3 5) (dy + 2b dx2 +y = 0 \dx) d²y dy + dx? 6) бу = 0 dx 7) x²y" + xy' + (x? – n²)y = 4x³

Q: A particle moves in the xY plane so that at any time 0 <t < 4, x = 2 cos t and y =t² + 3 sin t + 5…

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Q: 5) Consider four points A, B, C, and D whose geometrical locations correspond to the corners of a…

A: We have to find out the potential difference at various points.

Q: 2 Solve this Di fferential equat ion by applying ( variation paramet ers) 4+y = y+y%3DSE c x

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Q: By approximately how much will f(x, y, z) = x cos(rz) – 4x – 3y sin(xz) + y - change if the point…

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Q: find 19. || xy cos y dA, R: -1 < x < 1, 0< y<T 20. y sin (x + y) dA, R: -T < x < 0, 0 < y < 21. et-y…

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Q: Find the solution of the IVP. y" + 3y' + 2y = 20 (sin t + 8 (t – 1)), y (0) = 1, y' (0) = –1

A: We solve the given initial value problem by using Laplace transform.

Q: Assuming the truss members only bear axial loads, the following set of 10 equations can be…

A: Assume the truss members only bear axial loads, the following set of 10 equations can be determined:…

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

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Q: Find the solution u(t, x) to the system Jau +30₂u+u²=0 for t≥0, 20, u(t = 0, x) = cos(x). Start by…

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Q: šiven r,(t)=sin5ti +cos 5tj+\t+2k and r,(t)=5ti+2k , calculate "[r, (0) •r, (0)]. dt

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Q: EXERCISES 2.6 SE - dr where E=(z,y,x) and C is given by x = cost, y= sint and z t,0sts2 Evaluate

A: By Bartleby policy I have to solve only first one as these 2 are unrelated problems

Q: A particle moves in the XY plane so that at any time -2 <t<1, x = 5 sin t and y = t² – 3 cost – 1.…

A: NOTE: Refresh your page if you can't see any equations. . the horizontal component is x=3

Q: 3. The work done W,to stretch a spring from its natural length to an extension of 2 meters Is given…

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Q: Use a chain rule to find the values of dz dz and dr Ir=6, 0=n/6 Ir=6, 0=n/6 if z = xye"/y, x = r cos…

A: In this question  we have to find the value of differentiation.

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: Verify that the indicătéd function is an exp for each solution. y" - 6y' + 25y = 0; y = e3x cos 4x…

A: Recall: (uv)'=u'v+uv' where u and v are the function of x

Q: Express the given parametrization in the form y = f(x) by eliminating the parameter. x = 5t + 2, y =…

A: Given

Q: Consider curve C at R parameterized by: r(t) = cos(2t) î + tf+2 sin(2t)k, with 0 stsT An expression…

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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: 5. Para calcular la transformada inversa de Laplace de la función 3s2 (s2+1)2 puede utilizarse el…

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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: Classify each of the following equations as to order and degree. dy + (ху — сos x)dx %3D 0 d²Q + R…

A: As per our guidelines, we are supposed to solve only first three subparts. Kindly repost other…

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: Consider the 2nd order equation 2²y+ Sin dy y² +y = Choose the ight assertion A) the linearized…

A: consider the 2nd order equation d2ydx2+sindydt+y2+y=0 this is a non linear homogenous differential…

Q: Find the Second appoximation for the System. X Sin y at (xo,,)= (1, 1). y=Cosx

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Q: The current in an electric circuit is given by the equation di Ri +L==0, dt - %3D where L and R are…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: d Jcose d cose 'cos(r sin 0)]= [e* Telcom sin(tsin 0)]. (i) Show that t. %3D dt

A: (b) (i) show that t·ddtet cosθ cost sinθ=ddθet cosθ sint sinθ consider left hand side  t·ddtet cosθ…

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

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Q: Solve the following equation: 4 - Urz = 0,0 < x < T,0 <t < ∞ u(0, t) = u(T, t) = 0 %3D | %3D %3D…

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Q: Suppose r(t) = cos(nt) i + sin(at) j + 5tk represents the position of a particle on a helix, where z…

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Q: using

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Q: Find the general soultion of the follwoing equations dy cos x + y = cos²x, 15

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: From a sketch of the direction field, what can one say about the behavior as x approaches +o of a…

A: dydx=3-y+1xTo Find: From a sketch of the directional field state the behavior as x approaches +∞ of…

Q: I + 24 Determine the set of points at which the funct ion F(r, y) = is continuo us. +e-y?

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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: Let y= ao+aqt+ azt? + azt³ + a,t4 + agt5 + agt6 +...... be the solution of d?y dy +y=tan-lt ; y(0) =…

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Q: Find the general soultion of the follwoing equations dy cos x + y = cos²x, dx *+ y = xy/3.

A: Differential equation

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: F(x, y) = (4xy +2)i + (6x²y +2e)j is conservative by finding a potential function f for F, and use f…

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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: (5) Under what Conditions is (ax+by) dx + (KX+LY)dy=o exact? selve the eXact equation,Ca, b,k, L…

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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: u(x, t) = ear+bt %3D 1 u(x, t) = -/at %3D

A: The given functions are ux,t=eax+bt and ux,t=1te-x2/at.

Q: The auxiliary roots of the auxiliary equation associated with a certain HLDE are m=±3, ±3i, ± 3i.…

A: Solution is given as below:

Q: 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…

A: We will use the approach of the method you mentioned.

Q: 7. Let F = (2r sin(y)e", x² cos(y)e", a² sin(y)e*). %3D Find along the path c:7 = (sin(t), t,…

A: Given F→=2xsinyez,x2cosyez,x2sinyez. Find ∫CF→·dr→ along the path c:r→=sint,t,cost,-π2≤t≤π2. From…

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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