Internal problem ID [7369]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 650.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)+4*x*diff(y(x),x)+(4*x^2+6)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-x^{2}} \cos \left (2 x \right )+c_{2} {\mathrm e}^{-x^{2}} \sin \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 37
DSolve[y''[x]+4*x*y'[x]+(4*x^2+6)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} e^{-x (x+2 i)} \left (4 c_1-i c_2 e^{4 i x}\right ) \\ \end{align*}