43.2.12 problem 7.3.101 (b)

Internal problem ID [6869]
Book : Notes on Diffy Qs. Differential Equations for Engineers. By by Jiri Lebl, 2013.
Section : Chapter 7. POWER SERIES METHODS. 7.3.2 The method of Frobenius. Exercises. page 300
Problem number : 7.3.101 (b)
Date solved : Monday, January 27, 2025 at 02:32:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 222

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

\[ y(x)\to c_1 e^{-\frac {2 i}{\sqrt {x}}} x^{3/4} \left (\frac {520667425699057 i x^{9/2}}{131941395333120}-\frac {21896102683 i x^{7/2}}{21474836480}+\frac {19100991 i x^{5/2}}{41943040}-\frac {3367 i x^{3/2}}{8192}-\frac {194208949785748261 x^5}{21110623253299200}+\frac {5189376335871 x^4}{2748779069440}-\frac {846810601 x^3}{1342177280}+\frac {205387 x^2}{524288}-\frac {273 x}{512}+\frac {13 i \sqrt {x}}{16}+1\right )+c_2 e^{\frac {2 i}{\sqrt {x}}} x^{3/4} \left (-\frac {520667425699057 i x^{9/2}}{131941395333120}+\frac {21896102683 i x^{7/2}}{21474836480}-\frac {19100991 i x^{5/2}}{41943040}+\frac {3367 i x^{3/2}}{8192}-\frac {194208949785748261 x^5}{21110623253299200}+\frac {5189376335871 x^4}{2748779069440}-\frac {846810601 x^3}{1342177280}+\frac {205387 x^2}{524288}-\frac {273 x}{512}-\frac {13 i \sqrt {x}}{16}+1\right ) \]