Internal problem ID [14797]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.8, page 203
Problem number: 23 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime } x +2 y=0} \] 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(diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-x^{2}-\frac {1}{6} x^{4}\right ) y \left (0\right )+x D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 25
AsymptoticDSolveValue[y''[x]-2*x*y'[x]+2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {x^4}{6}-x^2+1\right )+c_2 x \]