52.2.34 problem 36 (a)

Internal problem ID [8285]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. 6.3 SOLUTIONS ABOUT SINGULAR POINTS. EXERCISES 6.3. Page 255
Problem number : 36 (a)
Date solved : Monday, January 27, 2025 at 03:47:54 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{3} y^{\prime \prime }+y&=0 \end{align*}

Using series method with expansion around

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

✗ Solution by Maple

Order:=8; 
dsolve(x^3*diff(y(x),x$2)+y(x)=0,y(x),type='series',x=0);
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 294

AsymptoticDSolveValue[x^3*D[y[x],{x,2}]+y[x]==0,y[x],{x,0,"8"-1}]
 

\[ y(x)\to c_1 e^{-\frac {2 i}{\sqrt {x}}} x^{3/4} \left (-\frac {11100458801337530625 i x^{13/2}}{4611686018427387904}+\frac {1327867167401775 i x^{11/2}}{4503599627370496}-\frac {468131288625 i x^{9/2}}{8796093022208}+\frac {66891825 i x^{7/2}}{4294967296}-\frac {72765 i x^{5/2}}{8388608}+\frac {105 i x^{3/2}}{8192}+\frac {1149690375852815671875 x^7}{147573952589676412928}-\frac {232376754295310625 x^6}{288230376151711744}+\frac {33424574007825 x^5}{281474976710656}-\frac {14783093325 x^4}{549755813888}+\frac {2837835 x^3}{268435456}-\frac {4725 x^2}{524288}+\frac {15 x}{512}-\frac {3 i \sqrt {x}}{16}+1\right )+c_2 e^{\frac {2 i}{\sqrt {x}}} x^{3/4} \left (\frac {11100458801337530625 i x^{13/2}}{4611686018427387904}-\frac {1327867167401775 i x^{11/2}}{4503599627370496}+\frac {468131288625 i x^{9/2}}{8796093022208}-\frac {66891825 i x^{7/2}}{4294967296}+\frac {72765 i x^{5/2}}{8388608}-\frac {105 i x^{3/2}}{8192}+\frac {1149690375852815671875 x^7}{147573952589676412928}-\frac {232376754295310625 x^6}{288230376151711744}+\frac {33424574007825 x^5}{281474976710656}-\frac {14783093325 x^4}{549755813888}+\frac {2837835 x^3}{268435456}-\frac {4725 x^2}{524288}+\frac {15 x}{512}+\frac {3 i \sqrt {x}}{16}+1\right ) \]