Internal problem ID [13662]
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 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+\frac {y^{\prime }}{x -3}+\frac {y}{x -4}=0} \] With the expansion point for the power series method at \(x = 3\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 55
Order:=6; dsolve(diff(y(x),x$2)+1/(x-3)*diff(y(x),x)+1/(x-4)*y(x)=0,y(x),type='series',x=3);
\[ y \left (x \right ) = \left (\ln \left (x -3\right ) c_{2} +c_{1} \right ) \left (1+\frac {1}{4} \left (x -3\right )^{2}+\frac {1}{9} \left (x -3\right )^{3}+\frac {5}{64} \left (x -3\right )^{4}+\frac {49}{900} \left (x -3\right )^{5}+\operatorname {O}\left (\left (x -3\right )^{6}\right )\right )+\left (-\frac {1}{4} \left (x -3\right )^{2}-\frac {2}{27} \left (x -3\right )^{3}-\frac {7}{128} \left (x -3\right )^{4}-\frac {469}{13500} \left (x -3\right )^{5}+\operatorname {O}\left (\left (x -3\right )^{6}\right )\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 128
AsymptoticDSolveValue[y''[x]+1/(x-3)*y'[x]+1/(x-4)*y[x]==0,y[x],{x,3,5}]
\[ y(x)\to c_1 \left (\frac {49}{900} (x-3)^5+\frac {5}{64} (x-3)^4+\frac {1}{9} (x-3)^3+\frac {1}{4} (x-3)^2+1\right )+c_2 \left (-\frac {469 (x-3)^5}{13500}-\frac {7}{128} (x-3)^4-\frac {2}{27} (x-3)^3-\frac {1}{4} (x-3)^2+\left (\frac {49}{900} (x-3)^5+\frac {5}{64} (x-3)^4+\frac {1}{9} (x-3)^3+\frac {1}{4} (x-3)^2+1\right ) \log (x-3)\right ) \]