Internal problem ID [13653]
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 (a).
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)]`]]
\[ \boxed {\left (x -3\right )^{2} y^{\prime \prime }-2 \left (x -3\right ) y^{\prime }+2 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
Order:=6; dsolve((x-3)^2*diff(y(x),x$2)-2*(x-3)*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {\left (-x^{2}+9\right ) y \left (0\right )}{9}-\frac {x D\left (y \right )\left (0\right ) \left (x -3\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 28
AsymptoticDSolveValue[(x-3)^2*y''[x]-2*(x-3)*y'[x]+2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (1-\frac {x^2}{9}\right )+c_2 \left (x-\frac {x^2}{3}\right ) \]