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In Problems 13–32 use variation of parameters to solve the given nonhomogeneous system.
18.
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A First Course in Differential Equations with Modeling Applications (MindTap Course List)
- 1. Find the solution to the initial value problem 4x3 + 1 2у — 6 y(1) = 2. A. y = 3 – Vxª + x – 1 B. y = 2+ Vx³ + x – 2 C. y = 1+ Vx4 + x – 1 D. y = 4 – V4x³ + x – 1 E. y = V4³ + x – 1arrow_forwardExample 1. Show that the solutions of the following system of differential equations remain bounded as t 00: -uarrow_forwardSolve each second-order IVP. 1. y" + 2y – 15y = 0, y(0) = 2, /(0) = -6 . 2. y" + 6y' + 13y = 0, y(0) = -1, y (0) = 5 3. y" + 2y +y = 0, y(0) = 3, y'(0) = –1arrow_forward
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- 1. The Lotka-Volterra or predator-prey equations dU = aU – UV, dt (1) AP = eyUV – BV. dt (2) have two fixed points (U., V.) = (0,0), (U., V.) = (- :). The trivial fixed point (0,0) is unstable since the prey population grows exponentially if it is initially small. Investigate the stability of the second fixed point (U..V.) = 6:27 PM 3/3/2021 近arrow_forwardDetermine the solution of the initial value problem 1. 5y" +y' 2. y" + 4y' + 5y = 35e4*, у (0) — 0, у'(0) 3 —10 У (0) 3D — 3, у'(0) — 1 = -6x,arrow_forwardConsider the following initial value problem: Edit 1 y" + 8y + 15y = 8(t – 5) + u10(t); y(0) = 0, y(0) = = 4 a) Find the solution y(t). ("-") 1 (e-St – e 5) y(t) = 8. 1 -3(t-5) 1 –5(t–5) ult) X 2 1 e-5(t-10) 10 1 -3(t-10) 6. Ud(t) 15 where c = 5 and d 10arrow_forward
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