7.15.35 problem 35

Internal problem ID [491]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.3 (Regular singular points). Problems at page 231
Problem number : 35
Date solved : Monday, January 27, 2025 at 02:54:05 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

Using series method with expansion around

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 43

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

\[ y(x)\to c_1 \left (-120 x^5+24 x^4-6 x^3+2 x^2-x+1\right )+\frac {c_2 e^{\frac {1}{x}}}{x} \]