35.9.20 problem 10, using elementary method

Internal problem ID [6255]
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
Date solved : Monday, January 27, 2025 at 01:50:12 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 14

dsolve(diff(y(x),x$2)-4*x*diff(y(x),x)+(4*x^2-2)*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{x^{2}} \left (c_{2} x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 18

DSolve[D[y[x],{x,2}]-4*x*D[y[x],x]+(4*x^2-2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{x^2} (c_2 x+c_1) \]