73.25.18 problem 35.4 (d)

Internal problem ID [15726]
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 : 35.4 (d)
Date solved : Tuesday, January 28, 2025 at 08:06:04 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (-9 x^{4}+x^{2}\right ) y^{\prime \prime }-6 x y^{\prime }+10 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.073 (sec). Leaf size: 35

Order:=6; 
dsolve((x^2-9*x^4)*diff(y(x),x$2)-6*x*diff(y(x),x)+10*y(x)=0,y(x),type='series',x=0);
 

\[ y = c_{1} x^{5} \left (1+18 x^{2}+243 x^{4}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} x^{2} \left (12-108 x^{2}-2916 x^{4}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 38

AsymptoticDSolveValue[(x^2-9*x^4)*D[y[x],{x,2}]-6*x*D[y[x],x]+10*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 \left (243 x^9+18 x^7+x^5\right )+c_1 \left (-243 x^6-9 x^4+x^2\right ) \]