Internal problem ID [6756]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime }+x y^{\prime }+3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 43
dsolve(2*diff(y(x),x$2)+x*diff(y(x),x)+3*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (\sqrt {\pi }\, {\mathrm e}^{-\frac {x^{2}}{4}} \erfi \left (\frac {x}{2}\right ) \left (x^{2}-2\right )-2 x \right )+c_{2} {\mathrm e}^{-\frac {x^{2}}{4}} \left (x^{2}-2\right ) \]
✓ Solution by Mathematica
Time used: 0.149 (sec). Leaf size: 47
DSolve[2*y''[x]+x*y'[x]+3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} c_2 \left (x^2-2\right ) F\left (\frac {x}{2}\right )+c_1 e^{-\frac {x^2}{4}} \left (x^2-2\right )-\frac {c_2 x}{4} \\ \end{align*}