73.25.5 problem 35.2 (e)

Internal problem ID [15713]
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 (e)
Date solved : Tuesday, January 28, 2025 at 08:05:48 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 \left (x -2\right )^{2} y^{\prime \prime }-4 \left (x -5\right ) y^{\prime }+2 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 59

Order:=6; 
dsolve(3*(x-2)^2*diff(y(x),x$2)-4*(x-5)*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1-\frac {1}{12} x^{2}+\frac {1}{54} x^{3}+\frac {1}{648} x^{4}-\frac {1}{4860} x^{5}\right ) y \left (0\right )+\left (x -\frac {5}{6} x^{2}+\frac {23}{108} x^{3}+\frac {23}{1296} x^{4}-\frac {23}{9720} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 70

AsymptoticDSolveValue[3*(x-2)^2*D[y[x],{x,2}]-4*(x-5)*D[y[x],x]+2*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (-\frac {x^5}{4860}+\frac {x^4}{648}+\frac {x^3}{54}-\frac {x^2}{12}+1\right )+c_2 \left (-\frac {23 x^5}{9720}+\frac {23 x^4}{1296}+\frac {23 x^3}{108}-\frac {5 x^2}{6}+x\right ) \]