Internal problem ID [7472]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 753.
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 y^{\prime }+8 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.024 (sec). Leaf size: 53
dsolve(diff(y(x),x$2)-2*x*diff(y(x),x)+8*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (\left (-4 x^{3}+10 x \right ) {\mathrm e}^{x^{2}}+4 \sqrt {\pi }\, \left (x^{4}-3 x^{2}+\frac {3}{4}\right ) \erfi \relax (x )\right )+c_{2} \left (4 x^{4}-12 x^{2}+3\right ) \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 55
DSolve[y''[x]-2*x*y'[x]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{12} \left (\left (4 \left (x^2-3\right ) x^2+3\right ) \left (\sqrt {\pi } c_2 \operatorname {Erfi}(x)+3 c_1\right )-2 c_2 e^{x^2} x \left (2 x^2-5\right )\right ) \\ \end{align*}