QI Ifz = eIn(x² + 2y² -xsin y + 1) dz and ду Find

Q: Q.2) The basts of the equatioon y'' + y" = 0,are: b) 1,1.e a) 1,1.e c) 1, x,e²* d) 1,x.e" 0 about

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Q: Using substitution show y = 1+ Ce-t² is a solution to dy + 2ty = 2t dt

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Q: axy = with r, K, a, s, b>0. dt a) interpret what each term in the equation means, and…

A: Given: dxdt=rx(1-xk)-axy-----------(1)dydt=sy(1-ybx)------------(2)

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Q: sec² (w) - -dw 4w2 +1 10.

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Q: the Pollowing Cx-)CX-2) di So lVe DE 2. + y =X %3D

A: The given linear differential equation is Dividing both sides by (x-1)(x-2) The given differential…

Q: QI: Solve the equation u = 4 uxr 0<x< 5, Ost<00 that satisfies the conditions u(0, t) = 0, u(5, t) =…

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Q: proof that: b2 y | VB? - y? dy =Vb² – y? + sin b + c 2

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Q: intersecting tiner (xs+2t y +t 20646)and x=3-t ye2 2011+2t).

A: Concept which used in next step : Equation of plane passing through (x1,y1,z1)&amp; having direction…

Q: z dz In order to evaluate JA2 – 9 we use the substitution sec e I= 3 sec 0 9. I= -sec 0 4. I= sec 0

A: Indefinite integral by substitution method

Q: x+ 3 b. J, x2-3x- 10

A: Trapezoidal rule: ∫abf(x)dx =(h/2)[f(x0)+2f(x1)+2f(x2)+2f(x3)+.....+2f(xn-1)+f(xn)] where h=step…

Q: using Runge xy' = y lnx, y(2) = e in the domain of [2,4], also find y(2.8), y(3.6).

A: Given, xy'=ylnx   , y2=e in the domain of 2,4

Q: Find x and y in terms of a and b.     ax  +  by  =  1 bx  +  ay  =  1       (a2 − b2…

A: We multiply the first equation by b and the second equation by a. Then subtract them  Subtracting…

Q: Solve ty" + y' + ty = 0 gives that y (0) = 1. %3D

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Q: af Find the values at the point (-7, 3) if and dy 3 S(x, y) = 32x° + 5x²y" + y} – -

A: fx, y=3x5+5x2y3+y23-37 Differentiating wrt x, we get  fxx, y=15x4+10xy3⇒fx-7, 3=15-74+10-733fx-7,…

Q: xp dt of dy A particular solution X, where XeC1 -2t dt Select the correct answer.

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Q: dy If dx and y(2) = 5, then y А. х2 — у? %3D —-21 В. х2 + у? %3D 21 С. у2 — х? %3D11.5 D. x2 — у?…

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Q: 2. Y, = x is a selution of y-?+ =0. Find the general solution. %3D

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Q: 6z ry- (y² zi + j+k) -i do 6.

A: The surface is defined as, x2+y2=42z=1z=7 The plot is a circular quadrant as observed in the…

Q: x(t) = (e-tcos2t – 5e-24)u(t) +,e²tu(-t) %3D 2

A: Given: xt=e-t cos 2t -5e-2tut+π2e2tu-t

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A: In difference equation  yt+k=Ekyt ϕEyt=gt y=C.F+P.I C.F=ϕEyt=0 P.I=1ϕEgt ∆c=0 where c is constant.

Q: lecessary steps. (a) / = V2r – 1 dz (b) ; dr edr +1

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Q: Solve y'"+ 5y' + 4y = 0, y(0) = - 8, y'(0) = 17 y(t) = %3D

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Q: ty" – t(t + 2)y' + (t + 2)y = 0, %3D

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Q: sec xdy – 4sin xsec ydx = 0; y 2 2 II

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Q: ii. (x + y)dA Where R = {(z, y)|1 < x² + y? < 4, x < 0}

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Q: rcosck) X)= 2メ+ hca) + ě Uf)→ at メ=3 @ fiw) = O (fuda (x)

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Q: %3D Given: 40 elx [y"-y'] = (x+1)(1-e'2X); determine; А) Ур В) Ус

A: Given 40eixy''-y'=x+11-ei2x

Q: Y; = pY;-1 (Y1, Y2, Y3)™. What ar

A: suppose that ε is N3(0,σ2I3) and Y0~N(0,σ20), independently from εi where i=1,2,3…

Q: yi+ yž = 1, when x = 0, y = 4 %3D %3D

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Q: u? – 1 du J2x u² + 1 3x - 56. g(x) :

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Q: Solve y'+ 8y' + 15y = 0, y(0) = 5, y'(0) = 19 | y(t) = %3D

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Q: y = e* - Tese x. What is y'= TescX %3D y!? 2. నా

A: Given, y=ex-πcscx We have to find y'.

Q: Find dy. 3 y = x³ (15-47) dy = (Simplify your answer.)

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Q: 2(х — Уjах + (3 — о when y(0)

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Q: d²v of cot w = 3v + 2w dw² Find %3D

A: Consider the equation cot w=3v+2w To find the derivative dvdw, differentiate the given equation…

Q: y = x"-9 (x 20) X=0, y=D, about the Xaxis %3D

A: To find the volume of curve , towards the rotation about x - axis.

Q: cose r cose r dz dr de r2 T/2 T/64 TU4 T/16

A: As per our guidelines, I can answer maximum one question and three subparts of a question. So here…

Q: lim (2,y)→(1,1) 2a2 – ry – y? 2² – y?

A: Evaluate the limit

Q: II. Find the value of x and y. 1. 4x + j(3y + 4) = 21 + j7 2. 3x + y + j(2x + 2y) = 13 + j10

A: Given equations are 1.  4x+j3y+4=21+j72.  3x+y+j2x+2y=13+j10 Solving for x and y.

Q: Solue For X: Y= Xト メ+xt Ixt

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Q: Y= 1/9 cot (3x-4) Y”=?

A: Here we will use simple standard results of derivatives to find double derivative of the function

Q: Q.2 Use ODE methods to solve the PDE: U-U₁5, U₁(x,0)=3x², U(0,y)=0 *****

A: Introduction: There are many different approaches that are useful to solve a partial differential…

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Q: solve for x and y: xy-x =0

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Q: max -a? – ry-y? r - 2y <-1 2.r + y 2 2

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Q: Solution 2 (i) f(x,y)=5x'e" +3xy– 2x' +3ху - 2х° of of ây дхду дудх

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Q: et2-2 2.2 R dxdy, where R between x2 = -y, y = 0 and x = -3 , y = -9 %3D

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