Internal problem ID [7093]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 364.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+2*x^2*diff(y(x),x)+(x^4+2*x-1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-\frac {x \left (x^{2}-3\right )}{3}}+c_{2} {\mathrm e}^{-\frac {x \left (x^{2}+3\right )}{3}} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 34
DSolve[y''[x]+2*x^2*y'[x]+(x^4+2*x-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{-\frac {1}{3} x \left (x^2+3\right )} \left (c_2 e^{2 x}+2 c_1\right ) \\ \end{align*}