73.25.11 problem 35.3 (e)

Internal problem ID [15719]
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 : 35.3 (e)
Date solved : Tuesday, January 28, 2025 at 08:05:55 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

\begin{align*} 4 \end{align*}

✓ Solution by Maple

Time used: 0.054 (sec). Leaf size: 250

Order:=6; 
dsolve(diff(y(x),x$2)+1/(x-3)^2*diff(y(x),x)+1/(x-4)^2*y(x)=0,y(x),type='series',x=4);
 

\[ y = \sqrt {x -4}\, \left (c_{2} \left (x -4\right )^{\frac {i \sqrt {3}}{2}} \left (1-\frac {1}{2} \left (x -4\right )+\frac {5 i \sqrt {3}+7}{8 i \sqrt {3}+16} \left (x -4\right )^{2}-\frac {1}{12} \frac {5+36 i \sqrt {3}}{\left (i \sqrt {3}+3\right ) \left (i \sqrt {3}+2\right )} \left (x -4\right )^{3}+\frac {1}{96} \frac {1313 i \sqrt {3}-865}{\left (i \sqrt {3}+4\right ) \left (i \sqrt {3}+3\right ) \left (i \sqrt {3}+2\right )} \left (x -4\right )^{4}+\frac {1}{480} \frac {23995 i+15978 \sqrt {3}}{\left (i \sqrt {3}+5\right ) \left (-\frac {\sqrt {3}}{2}+i\right ) \left (i \sqrt {3}+3\right ) \left (i \sqrt {3}+4\right )} \left (x -4\right )^{5}+\operatorname {O}\left (\left (x -4\right )^{6}\right )\right )+c_{1} \left (x -4\right )^{-\frac {i \sqrt {3}}{2}} \left (1-\frac {1}{2} \left (x -4\right )+\frac {5 \sqrt {3}+7 i}{8 \sqrt {3}+16 i} \left (x -4\right )^{2}+\frac {5-36 i \sqrt {3}}{-36+60 i \sqrt {3}} \left (x -4\right )^{3}+\frac {-1313 \sqrt {3}+865 i}{288 i-2208 \sqrt {3}} \left (x -4\right )^{4}+\frac {-23995-15978 i \sqrt {3}}{26880 i \sqrt {3}+20160} \left (x -4\right )^{5}+\operatorname {O}\left (\left (x -4\right )^{6}\right )\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 2225

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

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