chemical engineering mathematic

1. SOLUTION OF ORDINARY DIFFERENTIAL EQUETION
GROUP 2
Created By :
Rachma Amelinda (21315105024)
Hafan Rofiq Syahnur (21315105025)
Fidianto Suryana (21315105032)
Nurul Hesti Seftiyani (21315105036)
Yeni Variyana (21315105037)

2. Obtain the general solution of the following
differensial equations, valid near x=0

4. Function
a1(x) = x a1(0) = 0
a2(x) =1 a2(0) = 1
Function a1(x) and a2(x) is regular for x0=0
When the derivatives are :
When X0 = 0
(formula 2-13)
Ordinary

5. When the derivatives are :

6. [0 + 0 + 2A2 + 6A3.x + 12A4.x2 + 20A5.x3 + 30A6.x4 + 42A7.x5 +....] +
[0 + A1.x + 2A2.x2 + 3A3.x3 + 4A4.x4 + 5A5.x5 +....] +
[A0 + A1.x + A2.x2 + A3.x3 + A4.x4 + A5.x5 +...] = 0
From identity :
x0 : 2A2 + A0 = 0 A2 = -1/2 A0
X1 :6 A3 + 2A1 = 0 A3 = -1/3 A1
X2 :12A4 + 3 A2 = 0 A4 = -1/4 A2 = 1/8 A0
X3 :20A5 + 4 A3 = 0 A5 = -1/5 A3 = 1/15 A1
X4 :30A6 + 5 A4 = 0 A6 = -1/6 A4= 1/48 A0
X5 :42A7 + 6 A5 = 0 A7 = -1/7 A5= -1/105 A1
.............
..............

7. Finally solution is :
… … … … from (Equation 2-9)