Q1: Find 1) l (3 + e6t)2 2) e {e-3t(t + 1)²}

Q: (x2 – 1)y" – 2xy' + 2y = 0 - tion ofS the o uation

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Q: z2-ze coshw.K (z) z2– 2ze coshw.K+e2a -

A: The solution is given below. Hope this helps!

Q: - 4.9t tlut t600=0 t--14 士 + 4ベ49せo0 - 2<4:4 tz 12.59 tキーve

A: solution of quadratic equation is given by :when ax2+bx+c = 0x = -b±b2-4ac2a

Q: 2. Assume that x > -1. Prove that (1+ x)" >1+ nx for n = 0, 1, 2, ....

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Q: Show that kT| e-t²/kTdt = (kT)3/2 " 0. 2

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Q: 4. Is y = 5e-+7x e-2 a solution to the ODE y"+4y'+ 4y = 0 ?

A: The given solution is  y = 5e-x +7x.e-2x To verify it we will differentiate it

Q: (c) Show that V(3) = o²(X'V-¹X)-¹.

A: 3. c From the given information, y=Xβ+ε Eε=0, Vε=σ2V From the part b, β^=X'V-1X-1X'V-1y

Q: 3) FIND A PARTICULAR SOLUTION OF THE ODE y"+8y-20y = 2x +5 - e?X %3D

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Q: Calculate ∂ω/∂x for ω=e^−2x x(multiplied by) e^(z^2y)

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Q: 4.2 Apply the appropriate method to calculate the following: 1 = f***-8 I = S x2-4

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Q: Find a particular solution of (8) y′′′−4y′=t+3cost+e−2t.

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Q: Q1 Find root of equation f(x) = In (x')-5, using N-R method in [5,6] with e S0.0001, take E=|x1-x,…

A: Note: It is assumed that the N-R method is the Newton-Raphson method. The root of the equation…

Q: A quadratic equation x4-x-8=O is defined with an initial guess of 1 and 2. Find the approximated…

A: We need to find value of x2 using secant method.

Q: 10. dt 1+ 64t2 -1 A) 2sin-1 8 B) C) 2tan-1 D) 2tan-18 A B D.

A: Since you have asked multiple question,As per our policy we will solve the first question for you.…

Q: determine the second approximation Xz if Ne wtons Method was use to defermine the root o f the…

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Q: Find the general solution of y' + ny = emx for all m, n. Note: The case m = −n must be treated…

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Q: Fill in each blank so that the resulting statement is true.

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Q: 3t Q3) Verify that -e-3t e 3t are solution for re-3t 3t 1 e-3t -2 21 2 X on (-0, ∞). 2 X': -2 1 2 1

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Q: e 12t dt 31. 4et -1

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Q: m21 is nine times as large as m z2. Find mz1. -1 is supplementary to 2.

A: m∠1=9  m∠2                                       ------(1) and  m∠1+ m∠2=180°…

Q: (e) Yk+1 +Yk = 1/k(k+1),

A: Given, yk+1+yk=1kk+1Substitute:yk+1=y'yk=yEquation formed is:y'+y=1kk+1A first order separable ODE…

Q: 6/11 - 8) AT= 12 RT = 4x S. T %3D doesn't R

A: Given: A parallelogram STQR. As per the property of parallelogram, the diagonals bisect each other.…

Q: Ym - 21 , prove that + (n? m² ) yn =o 2 + (2n+1)x Ynts

A: Given y1/m+y-1/m=2x To prove that  x2-1yn+2+2n+1xyn+1+n2-m2yn=0 Solution :  y1/m+y-1/m=2x…

Q: Find the general Selution yer r the equatiJen S/0x)-14 ()+ 0 By(x) = =D0 dlax

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Q: :find E10 (-1)(n-1) Zn=1 (n+1)2 %3D1

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Q: Assume the model: Y = 5 - 2X + e , where e ~ N(0,81) What is the Pr(Y>10) when X =2? And What is…

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Q: the next iterative value of the of x² - 4 = O using secant method, if the initial guess is 3 and 4

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Q: 17. Solve the IVP: y" + 8y(v)? = 1, y(1) = 4, y'(1) = 1/4. Describe the procedure thoroughly and…

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Q: 3t when LI 1 ニe then L %3D S- 3 S-3

A: If Laplace transform of the function f(t) is denoted by Lf(t) or F(s), then the Laplace inverse of…

Q: find The Six Solutious of The eq- 6 Z+27+2

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Q: Also p; 2 0 for all j = {1, ., k} and E-1P; = 1. What is the value of E(X) and V(X)?

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Q: 6) Find most general antiderivative of the fxn. a) f(6) = x5+2x²-1 X' B) 4(1) - 2 +30*

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Q: Solve the equation using Reduction of Order y" -y = 2et Oy=c₁e¹ + c₂xet + e* (x + c3e-²x + C4)…

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Q: (i) Determine the number g, of ways of tossing a coin n times so that the combination HT never…

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Q: During a recession, Congress decides to stimulate the economy by providing funds to hire unemployed…

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Q: Q16 3 a) / 3²+ 2dt dt c) /,₁ (3-5)²

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Q: 4. Jordan and Jeffrey are driving north. Jordan is driving at 65 kph and Jeffrey is driving at 85…

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Q: (1+2 In æ)*

A: NOTE: Refresh your page if you can't see any equations. . ................(1) substitute…

Q: 1 y = [cosh(2x)] co* ot-1

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Q: Q4 Legendra polmomial Pe (X) =2 + (3x+1) than Prove that (2u+1) Puck) =Pmnil (X) -P(X) n-1

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Q: (a) In e7 (b) eln 2 %3D (c) eln v3 %3D Preview (d) In e5

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Q: Find the general solution of the ODE. y" + 4y' + 4y = x-?e-2* on (0, 0)

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Q: 5: A. Using convolution to find L¹ [(5+2)(s+4)

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Q: g) Suppose y² + [S(z)]² = 2, then (7,1)

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Q: 2 4 Mx(t) = -e+ 3t e' + e" + %3D 3 15

A: Given: Mxt=13et+415e3t+215e4t+415e5t

Q: Does y =e9-x2-2 exist?

A: Given an equation, y=e9-x2-2. To check whether the equation exists or not. The value of e is…

Q: 1 A. Using convolution to find L¹ [(5+2)(s+4)].

A: Convolution Theorem : If L-1F(s)=f(t) and L-1G(s)=g(t) then L-1F(s).G(s)=∫0tf(u).g(t-u)du. (As per…