35.9.13 problem 7, using series method

Internal problem ID [6248]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 12, Series Solutions of Differential Equations. Section 1. Miscellaneous problems. page 564
Problem number : 7, using series method
Date solved : Monday, January 27, 2025 at 01:50:03 PM
CAS classification : [[_Emden, _Fowler]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 25

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

\[ y = c_{1} x^{3} \left (1+\operatorname {O}\left (x^{6}\right )\right )+c_{2} x \left (-2+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 14

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

\[ y(x)\to c_2 x^3+c_1 x \]