78.19.17 problem 6

Internal problem ID [18436]
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 : 6
Date solved : Tuesday, January 28, 2025 at 11:50:01 AM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}}&=0 \end{align*}

Using series method with expansion around

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 17

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

\[ y(x)\to c_1 x+c_2 e^{\frac {1}{x}} x \]