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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
- 10. Use the Laplace transform to solve the system 1 - 4r +y 0. where r(0) = 2 and y(0) = 5 %3Darrow_forwardPROBLEM 2. Find the Fourier transform of f (t) = t 1arrow_forwardProblem 6.5 Find the Hamilton-Jacobi-Bellman equation for the sys- tem *1(t) = x2(t) i2 (t) = -2.x2(t) – 3x7(t)+ u(t) with the performance index as J = [" (-11) + u°(1) dt. stf 2arrow_forwardAdvanced mathsarrow_forward3. Use the Laplace transform method to solve the initial value problem x₁ = 6x₁ + 11x2, x2 = −4x1 - 9x2, with x₁(0) = 7 and x₂(0) = -1.arrow_forwardSolve 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_forwardHearrow_forwardQuestion No. 4: x²y' + xy = 1arrow_forwardIn some instances the Laplace transform can be used to solve linear differential equations with variable monomial coefficients. Use Theorem 7.4.1. THEOREM 7.4.1 Derivatives of Transforms If F(s) = L{f(t)} and n = 1, 2, 3,..., then L{t"f(t)} = (-1)"º F(s). ds" Reduce the given differential equation to a linear first-order DE in the transformed function Y(s) = L{y(t)}. Solve the first-order DE for Y(s) and then find y(t) = L{Y(s)}. ty" – y' = 4t2, y(0) = 0 y(t) =arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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