Internal problem ID [13658]
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: 35.2 (f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {\left (x -5\right )^{2} y^{\prime \prime }+\left (x -5\right ) y^{\prime }+4 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 54
Order:=6; dsolve((x-5)^2*diff(y(x),x$2)+(x-5)*diff(y(x),x)+4*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-\frac {2}{25} x^{2}-\frac {2}{125} x^{3}-\frac {7}{3750} x^{4}-\frac {1}{9375} x^{5}\right ) y \left (0\right )+\left (x +\frac {1}{10} x^{2}-\frac {1}{75} x^{3}-\frac {3}{500} x^{4}-\frac {1}{750} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 70
AsymptoticDSolveValue[(x-5)^2*y''[x]+(x-5)*y'[x]+4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {x^5}{9375}-\frac {7 x^4}{3750}-\frac {2 x^3}{125}-\frac {2 x^2}{25}+1\right )+c_2 \left (-\frac {x^5}{750}-\frac {3 x^4}{500}-\frac {x^3}{75}+\frac {x^2}{10}+x\right ) \]