59.1.22 problem 22

Internal problem ID [9194]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 22
Date solved : Monday, January 27, 2025 at 05:51:56 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 y^{\prime \prime }+x y^{\prime }+3 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 32

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

\[ y = \left (x^{2}-2\right ) \left (c_{1} \operatorname {erfi}\left (\frac {x}{2}\right ) \sqrt {\pi }+c_{2} \right ) {\mathrm e}^{-\frac {x^{2}}{4}}-2 c_{1} x \]

✓ Solution by Mathematica

Time used: 0.408 (sec). Leaf size: 52

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

\[ y(x)\to e^{-\frac {x^2}{4}} \left (x^2-2\right ) \left (c_2 \int _1^x\frac {e^{\frac {K[1]^2}{4}}}{\left (K[1]^2-2\right )^2}dK[1]+c_1\right ) \]