Internal problem ID [4897]
Book: ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG,
EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section: Chapter 5. Series Solutions of ODEs. Special Functions. Problem set 5.3. Extended Power
Series Method: Frobenius Method page 186
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {4 x y^{\prime \prime }+y^{\prime }+8 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 44
Order:=6; dsolve(4*x*diff(y(x),x$2)+diff(y(x),x)+8*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{\frac {3}{4}} \left (1-\frac {8}{7} x +\frac {32}{77} x^{2}-\frac {256}{3465} x^{3}+\frac {512}{65835} x^{4}-\frac {4096}{7571025} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (1-8 x +\frac {32}{5} x^{2}-\frac {256}{135} x^{3}+\frac {512}{1755} x^{4}-\frac {4096}{149175} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 83
AsymptoticDSolveValue[4*x*y''[x]+y'[x]+8*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (-\frac {4096 x^5}{149175}+\frac {512 x^4}{1755}-\frac {256 x^3}{135}+\frac {32 x^2}{5}-8 x+1\right )+c_1 x^{3/4} \left (-\frac {4096 x^5}{7571025}+\frac {512 x^4}{65835}-\frac {256 x^3}{3465}+\frac {32 x^2}{77}-\frac {8 x}{7}+1\right ) \]