Internal problem ID [7485]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 767.
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: 0.047 (sec). Leaf size: 53
dsolve(diff(y(x),x$2)-2*x*diff(y(x),x)+8*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (-4 \left (x^{4}-3 x^{2}+\frac {3}{4}\right ) \erfi \relax (x ) \sqrt {\pi }+{\mathrm e}^{x^{2}} \left (4 x^{3}-10 x \right )\right )+c_{2} \left (4 x^{4}-12 x^{2}+3\right ) \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 49
DSolve[y''[x]-2*x*y''[x]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {4 x-2} \left (c_1 I_1\left (4 \sqrt {x-\frac {1}{2}}\right )-c_2 K_1\left (4 \sqrt {x-\frac {1}{2}}\right )\right ) \\ \end{align*}