59.1.402 problem 414

Internal problem ID [9574]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 414
Date solved : Monday, January 27, 2025 at 06:04:15 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 y^{\prime \prime }+x y^{\prime }-4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 47

dsolve(3*diff(y(x),x$2)+x*diff(y(x),x)-4*y(x)=0,y(x), singsol=all)
 

\[ y = x c_{1} \sqrt {6}\, \left (x^{2}+15\right ) {\mathrm e}^{-\frac {x^{2}}{6}}+\left (x^{4}+18 x^{2}+27\right ) \left (\sqrt {\pi }\, \operatorname {erf}\left (\frac {\sqrt {6}\, x}{6}\right ) c_{1} +c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 43

DSolve[3*D[y[x],{x,2}]+x*D[y[x],x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{-\frac {x^2}{6}} \operatorname {HermiteH}\left (-5,\frac {x}{\sqrt {6}}\right )+\frac {1}{27} c_2 \left (x^4+18 x^2+27\right ) \]