36.6.2 problem 2

Internal problem ID [6363]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 8, Series solutions of differential equations. Section 8.4. page 449
Problem number : 2
Date solved : Monday, January 27, 2025 at 01:58:11 PM
CAS classification : [_Hermite]

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

Using series method with expansion around

\begin{align*} 2 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 72

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

\[ y = \left (1+\frac {3 \left (x -2\right )^{2}}{2}+\left (x -2\right )^{3}+\frac {9 \left (x -2\right )^{4}}{8}+\frac {3 \left (x -2\right )^{5}}{4}\right ) y \left (2\right )+\left (x -2+\left (x -2\right )^{2}+\frac {4 \left (x -2\right )^{3}}{3}+\frac {13 \left (x -2\right )^{4}}{12}+\frac {5 \left (x -2\right )^{5}}{6}\right ) y^{\prime }\left (2\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 79

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

\[ y(x)\to c_1 \left (\frac {3}{4} (x-2)^5+\frac {9}{8} (x-2)^4+(x-2)^3+\frac {3}{2} (x-2)^2+1\right )+c_2 \left (\frac {5}{6} (x-2)^5+\frac {13}{12} (x-2)^4+\frac {4}{3} (x-2)^3+(x-2)^2+x-2\right ) \]