In Problems 11–16 verify that the
16.
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A First Course in Differential Equations with Modeling Applications (MindTap Course List)
- This is the first part of a two-part problem. Let O 21 P = -2 sin(2t)] -2 cos(2t)]* cos(2t) y1(t) sin(2t)| ÿ2(t) = a. Show that 1(t) is a solution to the system i' = Pý by evaluating derivatives and the matrix product O 2] -2 Enter your answers in terms of the variable t. b. Show that y2(t) is a solution to the system i' = Pj by evaluating derivatives and the matrix product %(t) y2(t) Enter your answers in terms of the variable t.arrow_forward2) 3 3 dr+du+ +y=t dr subject to x = 1 and y = 0 at t = 0arrow_forwardThis is the first part of a two-part problem. Let P=[-: 1 5₁(t) = [(41) 5₂(t) = - sin(4t). a. Show that y₁ (t) is a solution to the system ÿ' = Pÿ by evaluating derivatives and the matrix product y(t) = = 0 [1] -4 Enter your answers in terms of the variable t. -4 sin(4t) -4 cos(4t)] ÿ₁ (t) [181-18] b. Show that y₂ (t) is a solution to the system ÿ' = Pÿ by evaluating derivatives and the matrix product Enter your answers in terms of the variable t. 04] 32(t) = [-28]|2(t) 181-181arrow_forward
- 7. Write down second-order linear equations of the form Ay" +By' + Cy=0 that are solved by the following functions: (a) y(t) = c₁e-t + c₂e-2t. (b) y(t) = et (c₁ cos(2t) + c₂ sin(2t)).arrow_forwardExample 1. Show that the solutions of the following system of differential equations remain bounded as t 00: -uarrow_forward9. P = 15 -4 -7 2e31 – 8e- -4e31 + 2e- ž(1) = | 3e3t – 20e- -6e31 + 5et Show that x1 (t) is a solution to the system x = Px by evaluating derivatives and the matrix product -4 ž(1) = | 15 -7 Enter your answers in terms of the variable t. Show that x2(t) is a solution to the system x' = Px by evaluating derivatives and the matrix product 9. 3(1) = | 15 -4 X2(t) -7 Enter your answers in terms of the variable t.arrow_forward
- Example 11.1. Classify the following equations : a²u 22u d²u du du +4. +4 J + 2- = 0 Əxdy oy² ax dy a²u •+ (1 - y²¹). = 0, -∞ < x ∞, -1arrow_forwardPart B: Consider the following problem max f(x,y) = (ry)² - x - 2y subject to h(x, y) = x²y-1 = 0. (x,y) ER² (d) Find all solutions to the problem [B]. Be mindful that (x, y) = R². [B]arrow_forward1page 6arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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