Internal problem ID [7795]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 308.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-2 x y^{\prime }+8 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 54
dsolve(diff(y(x),x$2)-2*x*diff(y(x),x)+8*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (\frac {4}{3} x^{4}-4 x^{2}+1\right )+c_{2} \left (\frac {4}{3} x^{4}-4 x^{2}+1\right ) \left (\int \frac {{\mathrm e}^{x^{2}}}{\left (4 x^{4}-12 x^{2}+3\right )^{2}}d x \right ) \]
✓ Solution by Mathematica
Time used: 1.113 (sec). Leaf size: 63
DSolve[y''[x]-2*x*y'[x]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \left (x^4-3 x^2+\frac {3}{4}\right )-\frac {1}{12} c_2 \left (\sqrt {\pi } \left (-4 x^4+12 x^2-3\right ) \text {erfi}(x)+2 e^{x^2} x \left (2 x^2-5\right )\right ) \]