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The current
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Determine the current as a function of time
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Chapter 7 Solutions
Fundamentals of Differential Equations and Boundary Value Problems
- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forwardIn Exercises 1-12, find the solution of the differential equation that satisfies the given boundary condition(s). x+4x+4x=0,x(0)=1,x(0)=1arrow_forwardThe following equation is derived from population genetics that specifies the evolutionary dynamics of the frequency of a bacterial strain of interest. dp sp(1 - p) p(0) = Po dt Find the solution, p(t). p(t) = =arrow_forward
- 3.Find the general solution of the third-order ODE y(³) + 6y" + 10y' + 6y = 0, note that m³ + 6m² +10m + 6 = (m + 2)³. Your Answer:arrow_forwardEliminate the arbitrary constantsarrow_forwardConsider the difference equation (with initial conditions y(-1), y(-2) provided below in the data) (n 20 and integer. Note: 6(n) is the unit impulse sample.): y(n) = ay(n – 1) – by(n – 2) +6(n) 1. Is the solution to this equation for n >0 stable ? Answer with reason(s). 2. What is the value of y(7) and limn-00 y(n) in the solution for y(n) Data: [y(-2), y(-1), a, b] = [-2.0, –-1.0,0.32, 0.2244]arrow_forward
- Given Y = c1eλ1tx1 + c2eλ2tx2 +· · ·+cneλntxn is the solution to the initial value problem: Y = AY, Y(0) = Y0 (a) show that Y0 = c1x1 + c2x2 +· · ·+cnxn (b) let X = (x1, . . . , xn) and c = (c1, . . . , cn)T. Assuming that the vectors x1, . . . , xn are linearly independent, show that c = X−1Y0.arrow_forward1 æ(0) = 2, y(0) = - 14 - 41 -8 æ(t) = y(t) =arrow_forward3. Find the initial value of f(t), if: 2(s + 2) s(s + 1)(s + 3) F(s)arrow_forward
- If B(p.q) = , tP-1(1-t)*-1 dt then prove that %3D 1 B(p = 1, q + 1) = 2 | t2p+1(1 – t²)ª dt.arrow_forwardA ball is thrown upward from the top of a 200-foot tall building with a velocity of 40 feet per second. Take the positive direction upward and the origin of the coordinate system at ground level. What is the initial value problem for the position, x(t), of the ball at time t?arrow_forwardA second-order chemical reaction involves the interaction of onc molccule of a substance P with one molecule of another substance Q to produce one molecule of another substance X. Suppose that p and q are the initial concentrations of P and Q and let r(t) be the concentration of X at time t. Then p- I(t) and q -r(t) are the concentrations of P and Q at time t, and the rate at which the reaction occurs is given by the equation dr *(I - b)(I – d)o= dt where a is a positive constant. Solve the initial value problem with r(0) = 0 assuming p # q. Answ: r(t) = Pq(e®(q-p)t _1 qea(q-p)t-p , you may nced to manipulate your answer to get this.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
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