59.1.79 problem 81

Internal problem ID [9251]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 81
Date solved : Monday, January 27, 2025 at 06:00:33 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 y^{\prime \prime }+5 x y^{\prime }+\left (2 x^{2}+4\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 22

dsolve(2*diff(y(x),x$2)+5*x*diff(y(x),x)+(4+2*x^2)*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-x^{2}} \left (c_{1} +\operatorname {erf}\left (\frac {i \sqrt {3}\, x}{2}\right ) c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.106 (sec). Leaf size: 42

DSolve[2*D[y[x],{x,2}]+5*x*D[y[x],x]+(4+2*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} e^{-x^2} \left (\sqrt {3 \pi } c_2 \text {erfi}\left (\frac {\sqrt {3} x}{2}\right )+3 c_1\right ) \]