73.25.9 problem 35.3 (c)

Internal problem ID [15717]
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 (c)
Date solved : Tuesday, January 28, 2025 at 08:05:52 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (-x^{4}+x^{3}\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+827 y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 1 \end{align*}

✓ Solution by Maple

Time used: 0.068 (sec). Leaf size: 62

Order:=6; 
dsolve((x^3-x^4)*diff(y(x),x$2)+(3*x-1)*diff(y(x),x)+827*y(x)=0,y(x),type='series',x=1);
 

\[ y = c_{1} \left (x -1\right )^{3} \left (1+\frac {409}{2} \left (x -1\right )+\frac {328391}{20} \left (x -1\right )^{2}+\frac {128327201}{180} \left (x -1\right )^{3}+\frac {19341852779}{1008} \left (x -1\right )^{4}+\frac {6949904889503}{20160} \left (x -1\right )^{5}+\operatorname {O}\left (\left (x -1\right )^{6}\right )\right )+c_{2} \left (\ln \left (x -1\right ) \left (567661070 \left (x -1\right )^{3}[phone] \left (x -1\right )^{4}+\frac {18641478643837}{2} \left (x -1\right )^{5}+\operatorname {O}\left (\left (x -1\right )^{6}\right )\right )+\left (12-4962 \left (x -1\right )+2059230 \left (x -1\right )^{2}-6162812 \left (x -1\right )^{3}-\frac {592298912511}{4} \left (x -1\right )^{4}-\frac {744988601770307}{40} \left (x -1\right )^{5}+\operatorname {O}\left (\left (x -1\right )^{6}\right )\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.065 (sec). Leaf size: 105

AsymptoticDSolveValue[(x^3-x^4)*D[y[x],{x,2}]+(3*x-1)*D[y[x],x]+827*y[x]==0,y[x],{x,1,"6"-1}]
 

\[ y(x)\to c_2 \left (\frac {19341852779 (x-1)^7}{1008}+\frac {128327201}{180} (x-1)^6+\frac {328391}{20} (x-1)^5+\frac {409}{2} (x-1)^4+(x-1)^3\right )+c_1 \left (\frac {1}{144} \left (-2226119942329 (x-1)^4-2270644232 (x-1)^3+24710760 (x-1)^2-59544 (x-1)+144\right )+\frac {283830535}{12} (409 (x-1)+2) (x-1)^3 \log (x-1)\right ) \]