Internal problem ID [13657]
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 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {3 \left (x -2\right )^{2} y^{\prime \prime }-4 \left (x -5\right ) y^{\prime }+2 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 54
Order:=6; dsolve(3*(x-2)^2*diff(y(x),x$2)-4*(x-5)*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-\frac {1}{12} x^{2}+\frac {1}{54} x^{3}+\frac {1}{648} x^{4}-\frac {1}{4860} x^{5}\right ) y \left (0\right )+\left (x -\frac {5}{6} x^{2}+\frac {23}{108} x^{3}+\frac {23}{1296} x^{4}-\frac {23}{9720} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 70
AsymptoticDSolveValue[3*(x-2)^2*y''[x]-4*(x-5)*y'[x]+2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {x^5}{4860}+\frac {x^4}{648}+\frac {x^3}{54}-\frac {x^2}{12}+1\right )+c_2 \left (-\frac {23 x^5}{9720}+\frac {23 x^4}{1296}+\frac {23 x^3}{108}-\frac {5 x^2}{6}+x\right ) \]