pls help Obtain the TSE of h(t) = 2t (1 + t)¯¹ in powers of (t – 1).-O-1 + (t-1)-(t − 1)² + (t − 1)³ –116(t-1)41O1+(t-1)-(t− 1)² + (t− 1)² –(t-1)4O1 + (t− 1) – (t − 1)² + § (t − 1)³ + 1/(t− 1)²1'1 + ½ (t − 1) + ½ (t − 1)² + § (t − 1)³ + ⁄⁄ (t − 1)416Question 4Use Laplace transforms to solve the differential equationy" +6y' + 13y = 0, given y(0) = 3 and y' = 7.y = e³x (3 cos 2x + 8 sin 2x)Oy=-e -3x (3 cos 2x + 8 sin 2x)-3xy=e-³² (3 cos 2x + 8 sin 2x)-3xOy=ey=e=³x (3 cos 2x 8 sin 2x)

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Obtain the TSE of h(t) = 2t (1+t)¯¹ in powers of (t – 1). - O-1 + ½(t-1)-(t − 1)² + ½ (t− 1)³ – ½⁄(t − 1)ª 1 O1+(t-1)-(t-1)² + (t-1)³ - 1 16 (t-1)4 1 + ½ (t − 1) − ½ (t − 1)² + § (t − 1)³ + ½ (t− 1)² 16