20.24.3 problem Problem 3

Internal problem ID [3988]
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 3
Date solved : Monday, January 27, 2025 at 08:05:48 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 37

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

\[ y \left (x \right ) = \left (1+x^{2}+\frac {1}{2} x^{4}\right ) y \left (0\right )+\left (x +\frac {2}{3} x^{3}+\frac {4}{15} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 38

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

\[ y(x)\to c_2 \left (\frac {4 x^5}{15}+\frac {2 x^3}{3}+x\right )+c_1 \left (\frac {x^4}{2}+x^2+1\right ) \]