Internal problem ID [4919]
Book: ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG,
EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section: Chapter 5. Series Solutions of ODEs. REVIEW QUESTIONS. page 201
Problem number: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {16 \left (1+x \right )^{2} y^{\prime \prime }+3 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 49
Order:=6; dsolve(16*(x+1)^2*diff(y(x),x$2)+3*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {3}{32} x^{2}+\frac {1}{16} x^{3}-\frac {93}{2048} x^{4}+\frac {9}{256} x^{5}\right ) y \relax (0)+\left (x -\frac {1}{32} x^{3}+\frac {1}{32} x^{4}-\frac {57}{2048} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 63
AsymptoticDSolveValue[16*(x+1)^2*y''[x]+3*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (-\frac {57 x^5}{2048}+\frac {x^4}{32}-\frac {x^3}{32}+x\right )+c_1 \left (\frac {9 x^5}{256}-\frac {93 x^4}{2048}+\frac {x^3}{16}-\frac {3 x^2}{32}+1\right ) \]