A series circuit contains a resistor with R = 10 ohms, an inductor with L = henries, a capacitor with C = farads, and an electromotive force E(t) = 300 volts. Find the particular 30 solution q, (i.e., the steady state solution) for the charge at time t.

Q: Find the solution. (D5 - 2D3 - 2D2- 3D - 2)y = 0. -3x y = (c,+c,x)e-*+c;e-+e*(c,cosx+c gsinxr) -2x A…

A: Given differential equation is (D5-2D3-2D2-3D-2)y = 0

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A: This is the problem of linearization, application of differential calculus.

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A: Given, three positive numbers whose sum is 18 and such that the sum of their square is as small as…

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A: To find the solution of a given differential equation first we will convert it into the form of…

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Q: (d) If v is an eigenvector for a matrix A and a matrix B then v is an eigenvector for A+ B.

A: TrueJustification:Suppose v is an eigenvector for a matrix A and a matrix B.Then there exist real…

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Q: Question 10 Theorem: There is no smallest positive rational number. A proof by contradiction of the…

A: A proof by contradiction always starts with the negation of the given statement to prove.

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Q: Relationship y= (ax+bX) - Find the Linearizationof Nonlinear

A: This is the question from linearization techniques. It involves the application of differential…

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Q: 7x° + 2+ 3x° log x +3x +2.x° log x+ 2x + 6x°

A: This is a problem of complexity.

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Q: 3. Let F(n) = 9F(n – 1) – 24F(n – 2) + 20F(n – 3) with initial conditions F(0) = 1, F(1) = 5 and…

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Q: Find the solution. d³x d?x dx -2-=0 di + di A y =c,e+c y = c+ O y = c,+cc'+ce2

A: Given differential equation is d3xdt3 + d2xdt2 - 2dxdt = 0

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Q: 34. (a) Find a parametric representation for the torus obtained by rotating about the z-axis the…

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Q: 1. Are the following matrices diagonalisable? Explain your answer. 2 0 50 1] a) A =-2 3 -1 -2 0 3 c)…

A: A matrix is diagonalizable if and only if for each eigenvalue the dimension of the eigenspace is…

Q: Σ (n:)? The radius of convergence of the series (x- 2)2 is equal to ........ n=1 3" (2n) !

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Q: (b) How to remove subtractive cancellation from the expression below: /20000. 0001 – V20000. 0000

A: Given expression is 20000.0001-20000.0000   Subtraction of two numbers of similar magnitude gives…

Q: QUESTION 1 Given a differential equation (3+x²) + 2.xy= (3 +x² )x² dx (а) Solve the differential…

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A: This is a problem of line integral.

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Q: e" + e-u 41 Use the substitution x = 2 with u 0, to evaluate dx. 42 A hird in flrime n

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Q: the matrix -2 -3

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Q: 7x +2+3x° log x +3x + 2x° log x + 2x'+ 6x 3

A: This is a problem of algorithm, complexity, function and run time.

Q: Find the Laplace Transform of e 2 cos3t + 5e 2 sin3t - s+2 + s2+9 15 A. g²+9 (s+2) + 15 (s2+4s) + 13…

A: To find the laplace transform of given function first we will use the linearity property of laplace…

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Q: Solve 2y" + (x + 1)y' + 3y = 0 by means of a power series about xo = 2. Find the recurrence…

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Q: Find the Inverse Laplace Transform of (s+4)3 A ³(2cos21 + - sin2t) e-2(cos21+ -sin2t) (2cos21 +…

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Q: Express the following permutation as a product of disjoint cycles. ). 1 2 3 4 5 6 7 8 9 10 11 12 f 2…

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Q: (b) y = 4xª+(3+51)x³+5x²-(100+1)x-400. What is the slope of the tangent on this curve at x=2.5?

A: Given curve,  y= 4x4+(3+51)x3+5x2-(100+1)x-400 To find the slope of the tangent on this curve at…

Q: 2. Use zero- through fourth-order Taylor series expansions to predict f(2.5) for f(x) = ln x using a…

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Q: 9. Use the series solution to solve the problems. a. xy" +4y'-xy = 0

A: Since you have posted a multiple  question according to guildlines I will solve first   question…

Q: (1+t2) ds + 2t[st2 – 3 (1+12) ²]dt = 0; when t = 0, s = 2.

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Q: 2xージ f (x) : 33 Vx2 T sin 2x + Ve2x + 2x –- In e, x # 1 1-x (1–3t)5(t³-8) g(t). t # 2 2-t

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Q: The position vector for a particle moving on a helix is c(t) = (5 cos(t), 5 sin(t), t²) . Find the…

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Q: Suppose that a particle following the path c(t) = (t,t – 5t,0) flies off on a tangent at to = 3.…

A: Given:c(t) = (t2 , t3-5t , 0)

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Q: 2. List the amplitude, midline, and period of each of the following functions: (a) 3 cos(T/4 * x) –…

A: We will use standard form of equation  For y= a sin (bx+c) +d           or     y= a cos (bx+c) +d…

Q: 86s - 78 Find the Inverse Laplace Transform of +3)(s-4)(5s– 1) - 2e -+ 3e+e3 В 41 - 3e

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Q: ssint, 0<t < TI 0, t2 Tt , y(0) = 0 y'(0) = 0 5. Find the solution of the IVP y"+ y' +y : %3D

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Q: What is the general solution to the differential equation y - O + = dx? dx In(Ay – 2) = Ax + B y2 =…

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