Internal problem ID [13681]
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 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {\left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y=0} \] With the expansion point for the power series method at \(x = 3\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 62
Order:=6; dsolve((x-3)*diff(y(x),x$2)+(x-3)*diff(y(x),x)+y(x)=0,y(x),type='series',x=3);
\[ y \left (x \right ) = c_{1} \left (x -3\right ) \left (1-\left (x -3\right )+\frac {1}{2} \left (x -3\right )^{2}-\frac {1}{6} \left (x -3\right )^{3}+\frac {1}{24} \left (x -3\right )^{4}-\frac {1}{120} \left (x -3\right )^{5}+\operatorname {O}\left (\left (x -3\right )^{6}\right )\right )+c_{2} \left (\ln \left (x -3\right ) \left (-\left (x -3\right )+\left (x -3\right )^{2}-\frac {1}{2} \left (x -3\right )^{3}+\frac {1}{6} \left (x -3\right )^{4}-\frac {1}{24} \left (x -3\right )^{5}+\operatorname {O}\left (\left (x -3\right )^{6}\right )\right )+\left (1-\left (x -3\right )+\frac {1}{4} \left (x -3\right )^{3}-\frac {5}{36} \left (x -3\right )^{4}+\frac {13}{288} \left (x -3\right )^{5}+\operatorname {O}\left (\left (x -3\right )^{6}\right )\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 105
AsymptoticDSolveValue[(x-3)*y''[x]+(x-3)*y'[x]+y[x]==0,y[x],{x,3,5}]
\[ y(x)\to c_2 \left (\frac {1}{24} (x-3)^5-\frac {1}{6} (x-3)^4+\frac {1}{2} (x-3)^3-(x-3)^2+x-3\right )+c_1 \left (\frac {1}{36} \left (-11 (x-3)^4+27 (x-3)^3-36 (x-3)^2+36\right )+\frac {1}{6} \left ((x-3)^3-3 (x-3)^2+6 (x-3)-6\right ) (x-3) \log (x-3)\right ) \]