Nasab
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View Nasab as PDF for free.
More details
- Words: 338
- Pages: 2
Nama Kelompok: Dwi Kurniati Zaenab (105017000416) Rahmadini Husna (105017000434) Mas’udah (105017000468) Tugas Nilai Awal Syarat Batas Metode Deret y"+ y ' = 0 2a 2 + 6a3 x + 12a 4 x 2 + ....... + a1 + 2a 2 x + 3a3 x 2 + ..... = 0 (2a 2 + a1 ) + (6a3 + 2a 2 ) x + (12a 4 + 3a3 ) x 2 + ........ = 0 2a 2 + aa1 = 0 a1 2 6a 3 + 2a 2 = 0 a2 = −
2a 2 2 a a = − − 1 = 1 6 6 2 6 12a 4 + 3a3 = 0 a3 = −
a4 = −
3a3 a 3 a =− 1=− 1 12 12 6 24
maka : y = a 0 + a1 x + a 2 x 2 + a3 x 3 + a 4 x 4 + .... a1 2 a1 3 a1 4 x + x − x + ..... 2 6 24 x2 x3 x4 = a 0 + a1 x − + − + ...... 2 6 24 = a 0 + a1 x −
[
= a 0 + a1 1 − e − x = a 0 + a1 − a1e
]
−x
= A1 + A2 e − x Misal: a0 + a1 = A1
dan –a1 = A2
Metode Biasa (Integral) y"+ y ' = 0 Misal : d = D sehingga dy = Dy dx dx d2y d2 2 Sehingga = D2 y = D 2 2 dx dx y"+ y ' = 0 d 2 y dy + =0 dx 2 dx D 2 y + Dy = 0 ( D 2 + D) y = 0 D( D + 1) y = 0 D = 0atauD = −1 solusi : y = c1e 0 x + c 2 e − x y = c1 + c 2 e − x
2a 2 2 a a = − − 1 = 1 6 6 2 6 12a 4 + 3a3 = 0 a3 = −
a4 = −
3a3 a 3 a =− 1=− 1 12 12 6 24
maka : y = a 0 + a1 x + a 2 x 2 + a3 x 3 + a 4 x 4 + .... a1 2 a1 3 a1 4 x + x − x + ..... 2 6 24 x2 x3 x4 = a 0 + a1 x − + − + ...... 2 6 24 = a 0 + a1 x −
[
= a 0 + a1 1 − e − x = a 0 + a1 − a1e
]
−x
= A1 + A2 e − x Misal: a0 + a1 = A1
dan –a1 = A2
Metode Biasa (Integral) y"+ y ' = 0 Misal : d = D sehingga dy = Dy dx dx d2y d2 2 Sehingga = D2 y = D 2 2 dx dx y"+ y ' = 0 d 2 y dy + =0 dx 2 dx D 2 y + Dy = 0 ( D 2 + D) y = 0 D( D + 1) y = 0 D = 0atauD = −1 solusi : y = c1e 0 x + c 2 e − x y = c1 + c 2 e − x
