68.1.11 problem Problem 1.8(b)

Internal problem ID [14140]
Book : Differential Equations, Linear, Nonlinear, Ordinary, Partial. A.C. King, J.Billingham, S.R.Otto. Cambridge Univ. Press 2003
Section : Chapter 1 VARIABLE COEFFICIENT, SECOND ORDER DIFFERENTIAL EQUATIONS. Problems page 28
Problem number : Problem 1.8(b)
Date solved : Tuesday, January 28, 2025 at 06:15:48 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+4 y^{\prime }-y x&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.061 (sec). Leaf size: 32

Order:=6; 
dsolve(x*diff(y(x),x$2)+4*diff(y(x),x)-x*y(x)=0,y(x),type='series',x=0);
 

\[ y = c_{1} \left (1+\frac {1}{10} x^{2}+\frac {1}{280} x^{4}+\operatorname {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (12-6 x^{2}-\frac {3}{2} x^{4}+\operatorname {O}\left (x^{6}\right )\right )}{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 42

AsymptoticDSolveValue[x*D[y[x],{x,2}]+4*D[y[x],x]-x*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (\frac {1}{x^3}-\frac {x}{8}-\frac {1}{2 x}\right )+c_2 \left (\frac {x^4}{280}+\frac {x^2}{10}+1\right ) \]