Internal problem ID [8148]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 673.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 32
dsolve(2*x^2*diff(y(x),x$2)-x*(1+2*x)*diff(y(x),x)+2*(4*x-1)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (\frac {4}{63} x^{4}-\frac {4}{7} x^{3}+x^{2}\right )+\frac {c_{2} \operatorname {hypergeom}\left (\left [-\frac {9}{2}\right ], \left [-\frac {3}{2}\right ], x\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.098 (sec). Leaf size: 89
DSolve[2*x^2*y''[x]-x*(1+2*x)*y'[x]+2*(4*x-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \left (x^4-9 x^3+\frac {63 x^2}{4}\right )-\frac {4 c_2 \left (\sqrt {\pi } \left (-4 x^2+36 x-63\right ) x^{5/2} \text {erfi}\left (\sqrt {x}\right )+2 e^x \left (2 x^4-17 x^3+24 x^2+6 x+3\right )\right )}{945 \sqrt {x}} \]