78.19.1 problem 1 (a)

Internal problem ID [18420]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 5. Power Series Solutions and Special Functions. Section 29. Regular singular Points. Problems at page 227
Problem number : 1 (a)
Date solved : Tuesday, January 28, 2025 at 11:49:44 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 80

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

\[ y(x)\to c_2 e^{-\frac {1}{x^2}} \left (-\frac {51 x^5}{40}+\frac {63 x^4}{32}+\frac {x^3}{2}-\frac {3 x^2}{4}+1\right ) x^3+c_1 \left (-\frac {9 x^5}{40}-\frac {9 x^4}{32}-\frac {x^3}{2}-\frac {3 x^2}{4}+1\right ) \]