46.5.4 problem 14

Internal problem ID [7340]
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
Date solved : Monday, January 27, 2025 at 02:50:41 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 16 \left (1+x \right )^{2} y^{\prime \prime }+3 y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 54

Order:=6; 
dsolve(16*(x+1)^2*diff(y(x),x$2)+3*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1-\frac {3}{32} x^{2}+\frac {1}{16} x^{3}-\frac {93}{2048} x^{4}+\frac {9}{256} x^{5}\right ) y \left (0\right )+\left (x -\frac {1}{32} x^{3}+\frac {1}{32} x^{4}-\frac {57}{2048} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 63

AsymptoticDSolveValue[16*(x+1)^2*D[y[x],{x,2}]+3*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 \left (-\frac {57 x^5}{2048}+\frac {x^4}{32}-\frac {x^3}{32}+x\right )+c_1 \left (\frac {9 x^5}{256}-\frac {93 x^4}{2048}+\frac {x^3}{16}-\frac {3 x^2}{32}+1\right ) \]