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Q: a=t). CTaylon Serie) 2-X Ln +x) (MacLurinSeries

A: We need to find the Taylor series of f(x)=12-x at a=1. Taylor series of function fx at a is defined…

Q: 23 4- [fe** dycdx ans :(e' - e' )(e² – e') 12

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Q: Can i get help step by step?

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Q: x2+1 =0 Has soluion in R

A: Solution:

Q: If z' + In(e el + e²) = 0 dz find ar at the point (0, 0) O 3 0 -3 O 2 O-2 « Previous

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Q: Example 7.13. Apply Bessel's formula to obtain y25 given y20 2854, y24 = 3162, y 28 = 3544, y 32 =…

A: Here we need to use bessel's formula to solve this problem.

Q: y' - y y2

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Q: 2. Consider the initial value problem (IVP) { (t +1)(t – 1)(t- 2) t e"y y(.5) - cos t? %3D 1 Use…

A: Furst we rewrite the equation as in the theorem, then Use the given theorem

Q: 1 1 lim t->0 tv1+t t ou upload at the end of this c

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Q: /9 – 2° dz Integrate: z4

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Q: 7. Solve the following first-order linear DE's. y' + (cotx)y = xcscx, ) = 1

A: As per our guidelines we are allowed to do 1 question at a time. Please post other questions next…

Q: find the Solehion dy'= 4t + 2e

A: Given the differential equation :

Q: 1 О. 15 Show that %3D (D - Q) k e k

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Q: 4x obtain the section of the equation Ex xl with the condition u oon X4

A: Let us consider the given PDE is P(x,y,u)ux+Q(x,y,u)uy=R(x,y,u) The equation is solved as Determine…

Q: 1 Find the general Solution of the following equa tion ; xy'-2y=x²

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: X= Sv-6u+sw, y=2u-2v+ 3w and z=8u-bvt 10w implics a (x,y,z)

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Q: Solve the difference equation In+2 + In+1 – 2.x, = 0 subject to the initial conditions ro = 1 and r…

A: To find- Solve the difference equation xn+2 + xn+1 - 2xn = 0 subject to initial conditions x0 = 1…

Q: A radioactive sample decays according to the law - -hy where k>0 Suppose c represents the size of…

A: From the given differential equation:   dydt=-ky   So, dy=-kydt...Integrating on both…

Q: 1)z = e(4+j3) In(6230") 2) z = (-;)(* 2) z = (-)(r)"

A: (1) The  given complex equation is                                                Z=e4+j3ln6∠30°

Q: 21 Determine the form of a particular solution for the ODE y" + 4y= 3sin2t + te

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Q: Posses ho solurion forr fcs)=S but That Posseses infinitly many solutions whcn f(s) =l

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Q: 1) Evalúe a) csch (In 3) b) cosh (0)

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Q: 12. Solve the problem: Utt = c*upx + Ax, 0 0, A= constant, и (х,0) — 0, и (0, t) — 0, Ut (x, 0) =…

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Q: 4) We know that () and a!=1.2...a. Prove that Yn75, )< 2n-2. G0od Luck!

A: Given, ab=a!(a-b)!b! and a!=1.2....a

Q: In 3 e'dt 0 ve Ve2t+4

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Q: Determine the general solution of the following Bernoulli ODE: y' + xy = x³y³

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Q: If 8(x) = [e²-m (21+ - dx S[e²-In (21+1) ]dt, find g(x). -2 A e-In(2x+1) 4 B (2x + 1)² 2 Ⓒ (2x + 1)²…

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Q: 4 Σ E Vn +1 n=-1

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Q: •1 cln(5) 1- S SmS) xy evx ´dydx r

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Q: Eva 6 SSin'z osx dy

A: ∫undu=un+1n+1.     cos2x+sin2x = 1

Q: 2. Find all equilibrium or constant solutions (if any) to the ODE below dp dq dp dq 3

A: In this question, the constant solution of a differential equation is to be determined. Constant…

Q: 2) Show that L(1-x*)P",)P"mx) dx = 21(1+ 1) Sim 21 +1

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Q: 1 if Pn (x) dx32 . then n= -1 0.a o none of theseco -1do

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Q: Solve the Cauchy-Euler initial value problem (2 x² y" – x y' + y = x, x>0, y(1) = 0, y'(1) = 0. Find…

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Q: 6. 81n V81 - 81 – x²dx 4 A. Show that B. Use (A) to evaluate In 4 (e2x – e*) /81 – (e* – 1)* dx. - -

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Q: 5. Solve the problem kuxx = xt, u(x,0) = 0, u₁(x,0) = e, Utt - kuxx -∞ 0 ∞ < x < ∞ ∞<x<∞ -

A: Given is the pde. The objective is to find the solution. The solution is for this type of pde is…

Q: (4) The general solution to (x +3)y" +5xy' - y = 0 converges at least on and is y = Co x2+ r6 +...…

A: 4.  We have differential equation x2+3y''+5xy'-y=0  now take a power series y=∑n=0∞cnxn…

Q: 25-30 Find dz/ax and dz/ay. 25. z = 4e+3y

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Q: Question 4 4.1.a q(t) = t°In(t³) q(1) = 2t In(e*) + *(: 2 5t 5 2t In In (t) + 5t

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Q: c). Invest diFrgate whether the given en equation is homogene eous dy 2. oxy

A: A first order differential equation is homogeneous when it can be written as a function of y/x, that…

Q: You're to find x in the second question. Thanks

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Q: 16. (x – y ln y + y ln x) dx + x(ln y – In x) dy = 0. ) In

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Q: d If g(x)=- S* [e²-In (21+1) ]dt, find g(x). -2 2 (2x + 1)2 4 B (2x + 1)² Ⓒe-In(2x+1) 4 (2x + 1)² di…

A: A function is given by, gx=ddx∫-2xet-ln2t+1dt. The objective is to find the second derivative g''x…

Q: {In(8n+1) – In(4n +5)} 20. b. 0 c. In(2) d. In(5) e. Divergent а. 2 с.

A: ln8n+1-ln4n+5 Now, limn→∞ln8n+1-ln4n+5=limn→∞ln8n+14n+5…

Q: # 8.) (8 # dy + Bernoulli s D.E, dx - 3xy2 dx =0> DET. THE GEN, soL'N OF THE D.E.

A: As we know that; The standard form of Bernoulli's equation is; dydx+Py=Qyn Where; P&amp; Q is the…

Q: 4 In(t) dt

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Q: 9. 3cos(@t – a), where w and a are constants.

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Q: (3) 1. Solve the IVP u +u"=e*-7 tx with y(0)=1, y'(0)=0, y"(0)=1 (where t is a real constant)

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Q: 2.7 where t is the time in months after the virus was first detected. 1+14e 0.761'

A: Here we have,  The number of computer N(t) (in millions) infected by a computer virus is,

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.