Internal problem ID [7512]
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]]
\[ \boxed {2 y^{\prime \prime }+x y^{\prime }+3 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 47
dsolve(2*diff(y(x),x$2)+x*diff(y(x),x)+3*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-\frac {x^{2}}{4}} \left (x^{2}-2\right )+c_{2} {\mathrm e}^{-\frac {x^{2}}{4}} \left (x^{2}-2\right ) \left (\int \frac {{\mathrm e}^{\frac {x^{2}}{4}}}{\left (x^{2}-2\right )^{2}}d x \right ) \]
✓ Solution by Mathematica
Time used: 0.333 (sec). Leaf size: 61
DSolve[2*y''[x]+x*y'[x]+3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{8} e^{-\frac {x^2}{4}} \left (\sqrt {\pi } c_2 \left (x^2-2\right ) \text {erfi}\left (\frac {x}{2}\right )+8 c_1 \left (x^2-2\right )-2 c_2 e^{\frac {x^2}{4}} x\right ) \]