Internal problem ID [4403]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 12, Series Solutions of Differential Equations. Section 1. Miscellaneous problems. page
564
Problem number: 10, using elementary method.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve(diff(y(x),x$2)-4*x*diff(y(x),x)+(4*x^2-2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x^{2}}+c_{2} {\mathrm e}^{x^{2}} x \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 18
DSolve[y''[x]-4*x*y'[x]+(4*x^2-2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{x^2} (c_2 x+c_1) \\ \end{align*}