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In Problems 21–24, solve the given initial value problem using the method of Laplace transforms. Sketch the graph of the solution.
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Chapter 7 Solutions
Fundamentals of Differential Equations and Boundary Value Problems
- Problem 2 a. If y(t) = x₁(1) * x₂ (t)= e(+3)u(t+3), find z(t) = x₁(1+4)*x₂(t-5). b. If x₁ (1) = 8e²¹u(-1) and x₂(t)=0.258(1-4), find y(t)=x (t)* x₂(t). c. If x₁(t) = 4e-2¹u(t) and x₂ (1)= u(1), find y(t) = x₁(1) * x₂ (1)arrow_forwardQUESTION 3 Identify the order k of the Legendre equation (1-x²)y" - 2xy + 20y=0 with general solution y(x) = C₁y₁ + C₂y₂. Hence, use the Legendre generating function to approximate the value of Pk (1).arrow_forwardExample 10.11. Using modified Euler's method, find y(0.2) and y(0.4) given y = y + e*, y(0) = 0.arrow_forward
- Solve the given initial value problem using the method of Laplace transforms. Sketch the graph of the solution. w" +w= 2u(t - 2) – 3u(t - 5); w(0) = 1, w'(0) = 0arrow_forwardSuppose solving an equation by Laplace transform results in 6 s Y(s) = s2 + 64° Evaluate y(r).arrow_forwardExample 1: A particle is moves along a coordinate axis in the positive direction to the right. Its position at time t' is given by s(t) = t³ – 4t + 2. Find v(1) and a 1), use these to answer the following questions: (a). Is the particle moving from left to right or from right to left at t =1? (b). Is the particle speeding up or slowing down at time t 1? Solution:arrow_forward
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