73.25.2 problem 35.2 (b)

Internal problem ID [15710]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 35. Modified Power series solutions and basic method of Frobenius. Additional Exercises. page 715
Problem number : 35.2 (b)
Date solved : Tuesday, January 28, 2025 at 08:05:45 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.047 (sec). Leaf size: 22

Order:=6; 
dsolve(2*x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
 

\[ y = \frac {c_{1} \sqrt {x}+c_{2} x}{x^{{3}/{2}}}+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 18

AsymptoticDSolveValue[2*x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to \frac {c_1}{\sqrt {x}}+\frac {c_2}{x} \]