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In Problems 13–32 use variation of parameters to solve the given nonhomogeneous system.
15.
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- Consider 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_forward1.3. Study the existence and uniqueness of the solution of the initial value problem (2y — 4)y' — (3x² − 4x − 4)(y² – 4y – 4) = 0, y(2) =-.arrow_forward1. Consider the accidental death model illustrated below. Let μ Alive 0 Dead-Accident Dead-Other Causes 2 10-5 and μ 7.4 x 10-5 and c = 1.05. Let = max (5,7). Calculate: (i) TP 00 (ii) po (iii)+p 01 A+ Bc for all x where A = 5 x 10-4, B =arrow_forward
- Q.8arrow_forwardQ. No. 11 The solution of the DE 3ry" + y/ – y = 0 (a) yı = rš[1 – {x +²+...], y2 = 1+x – 20² + ... (b) yı = a3[1 – r +a² + ...], y2 = 1+ 2x – 2x² + ... (c) yı = xš[1 – x + a² + ...], y2 =1+ 2x – 2x3 + ... (d) yı = [1 – x + x² + ...], y2 = 1+ 2x – 2x2 +... solve this and tick the correct optionarrow_forward5.2arrow_forward
- 3. The function y(x) = x³ – is a solution of which of the following initial value problems? (a) ry' + 3y = 6x³, y(1) = 0 (b) xy' + 3y = 0, y(1) = 0 (c) ry + 3y = 6x-³, (d) ry' + 3y = 0, y(0) = 0. y(1) = 0arrow_forward-4 -4 0 9 1 -4 -3 1 Problem 1: Let A = 10 1. Solve the initial-value problem x' Ax with x(0) = (2, 1,-1)". %3D 2. Find et 3. Use the method of variation of parameters to solve the initial-value problem x' = Ax + with x(0) = (0,0,0)".arrow_forwarden.c. 2. Solve the initial value problem y"-5y"+6y' = 0, y"(0) = 1, y'(0) = 0, y(0) = 1.arrow_forward
- Linear Methodsarrow_forwardQ. 67-75 Solve the initial value problems. dy 67. 2 – 7, y(2) = 0 dx 68. 10 - x, y(0) = -1 dx dy 69. - + x, > 0; y(2) = 1 dx 1-² dy 70. == 9x² - 4x + 5, y(-1) = 0 dx dy 71. = 3x-2/3, y(-1) = -5 dx dy 1 72. - y (4) = 0 dx 2Vx ds 73. = 1 + cost, s (0) = 4 dt 74. = cost + sint, s(7) = 1 -π sin 70, 7(0) = 0 1. / 126 + = = ds dt dr 75. d0 Evaluate the integrals in Exercises 13-36. 13. ·/₁ V3-2s ds 14. (2x + 1)³ dx Area In Exercises 37-42, fine x-axis. |37. y = -x − 2x, - 38. y = 3x²-3, -25 39. y=x²-3x² + 2 40. y = x² - 4x. -2 41. y = x¹/³, -1 s 42. y = x¹/3 - x, - 9. (a) Find the termi is (1, -2). (b) Find the initi point is (5, 0. 10. (a) Find the terr is (2, -1). (b) Find the ter point is (-2 11-12 Perform the and w. 11. u = 3i - k, v (a) w - v (c) -v - 2w (e) -8(v + w 12. u = (2,-1,3 (a) u - warrow_forwardExample 7.2. Find a solution of the following system of ODEs using method of variation of parameters. Use y₁ (0): = 19 and y₂ (0) = -23. * = [6²1]+[A]* y' 3 5 5 etarrow_forward
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