20.24.6 problem Problem 6

Internal problem ID [3991]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 11, Series Solutions to Linear Differential Equations. Exercises for 11.2. page 739
Problem number : Problem 6
Date solved : Monday, January 27, 2025 at 08:05:50 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 39

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

\[ y \left (x \right ) = \left (1-\frac {3}{2} x^{2}+\frac {5}{8} x^{4}\right ) y \left (0\right )+\left (x -\frac {2}{3} x^{3}+\frac {1}{5} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 42

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

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