Internal problem ID [13684]
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: 35.5 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x -3\right )^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }-3 y=0} \] With the expansion point for the power series method at \(x = 3\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 49
Order:=6; dsolve((x-3)^2*diff(y(x),x$2)+(x^2-3*x)*diff(y(x),x)-3*y(x)=0,y(x),type='series',x=3);
\[ y \left (x \right ) = \frac {c_{1} \left (x -3\right )^{4} \left (1-\frac {1}{5} \left (x -3\right )+\frac {1}{30} \left (x -3\right )^{2}-\frac {1}{210} \left (x -3\right )^{3}+\frac {1}{1680} \left (x -3\right )^{4}-\frac {1}{15120} \left (x -3\right )^{5}+\operatorname {O}\left (\left (x -3\right )^{6}\right )\right )+c_{2} \left (-144+144 \left (x -3\right )-72 \left (x -3\right )^{2}+24 \left (x -3\right )^{3}-6 \left (x -3\right )^{4}+\frac {6}{5} \left (x -3\right )^{5}+\operatorname {O}\left (\left (x -3\right )^{6}\right )\right )}{\left (x -3\right )^{3}} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 81
AsymptoticDSolveValue[(x-3)^2*y''[x]+(x^2-3*x)*y'[x]-3*y[x]==0,y[x],{x,3,5}]
\[ y(x)\to c_1 \left (\frac {x-3}{24}+\frac {1}{2 (x-3)}-\frac {1}{(x-3)^2}+\frac {1}{(x-3)^3}-\frac {1}{6}\right )+c_2 \left (\frac {(x-3)^5}{1680}-\frac {1}{210} (x-3)^4+\frac {1}{30} (x-3)^3-\frac {1}{5} (x-3)^2+x-3\right ) \]