73.25.28 problem 35.4 (n)

Internal problem ID [15736]
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 (n)
Date solved : Tuesday, January 28, 2025 at 08:06:16 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (9 x^{3}+9 x^{2}\right ) y^{\prime \prime }+\left (27 x^{2}+9 x \right ) y^{\prime }+\left (8 x -1\right ) y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.057 (sec). Leaf size: 41

Order:=6; 
dsolve((9*x^2+9*x^3)*diff(y(x),x$2)+(9*x+27*x^2)*diff(y(x),x)+(8*x-1)*y(x)=0,y(x),type='series',x=0);
 

\[ y = \frac {\left (-x^{5}+x^{4}-x^{3}+x^{2}-x +1\right ) \left (x^{{2}/{3}} c_{2} +c_{1} \right )}{x^{{1}/{3}}}+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 62

AsymptoticDSolveValue[(9*x^2+9*x^3)*D[y[x],{x,2}]+(9*x+27*x^2)*D[y[x],x]+(8*x-1)*y[x]==0,y[x],{x,0,"6"-1}]
 

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