Internal problem ID [13661]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (-x^{4}+x^{3}\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+827 y=0} \] With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.0 (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);
\[ y \left (x \right ) = c_{1} \left (-1+x \right )^{3} \left (1+\frac {409}{2} \left (-1+x \right )+\frac {328391}{20} \left (-1+x \right )^{2}+\frac {128327201}{180} \left (-1+x \right )^{3}+\frac {19341852779}{1008} \left (-1+x \right )^{4}+\frac {6949904889503}{20160} \left (-1+x \right )^{5}+\operatorname {O}\left (\left (-1+x \right )^{6}\right )\right )+c_{2} \left (\ln \left (-1+x \right ) \left (567661070 \left (-1+x \right )^{3}+116086688815 \left (-1+x \right )^{4}+\frac {18641478643837}{2} \left (-1+x \right )^{5}+\operatorname {O}\left (\left (-1+x \right )^{6}\right )\right )+\left (12-4962 \left (-1+x \right )+2059230 \left (-1+x \right )^{2}-6162812 \left (-1+x \right )^{3}-\frac {592298912511}{4} \left (-1+x \right )^{4}-\frac {744988601770307}{40} \left (-1+x \right )^{5}+\operatorname {O}\left (\left (-1+x \right )^{6}\right )\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.067 (sec). Leaf size: 105
AsymptoticDSolveValue[(x^3-x^4)*y''[x]+(3*x-1)*y'[x]+827*y[x]==0,y[x],{x,1,5}]
\[ y(x)\to c_2 \left (\frac {19341852779 (x-1)^7}{1008}+\frac {128327201}{180} (x-1)^6+\frac {328391}{20} (x-1)^5+\frac {409}{2} (x-1)^4+(x-1)^3\right )+c_1 \left (\frac {1}{144} \left (-2226119942329 (x-1)^4-2270644232 (x-1)^3+24710760 (x-1)^2-59544 (x-1)+144\right )+\frac {283830535}{12} (409 (x-1)+2) (x-1)^3 \log (x-1)\right ) \]