7.15.29 problem 29

Internal problem ID [485]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.3 (Regular singular points). Problems at page 231
Problem number : 29
Date solved : Monday, January 27, 2025 at 02:54:03 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x y^{\prime \prime }+8 y^{\prime }+y x&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 32

Order:=6; 
dsolve(4*x*diff(y(x),x$2)+8*diff(y(x),x)+x*y(x)=0,y(x),type='series',x=0);
 

\[ y = c_1 \left (1-\frac {1}{24} x^{2}+\frac {1}{1920} x^{4}+\operatorname {O}\left (x^{6}\right )\right )+\frac {c_2 \left (1-\frac {1}{8} x^{2}+\frac {1}{384} x^{4}+\operatorname {O}\left (x^{6}\right )\right )}{x} \]

✓ Solution by Mathematica

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

AsymptoticDSolveValue[4*x*D[y[x],{x,2}]+8*D[y[x],x]+x*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (\frac {x^3}{384}-\frac {x}{8}+\frac {1}{x}\right )+c_2 \left (\frac {x^4}{1920}-\frac {x^2}{24}+1\right ) \]