Internal problem ID [7392]
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]]
Solve \begin {gather*} \boxed {2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+2 \left (4 x -1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.167 (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)
\[ y \relax (x ) = c_{1} \left (\frac {4}{63} x^{4}-\frac {4}{7} x^{3}+x^{2}\right )+\frac {c_{2} \hypergeom \left (\left [-\frac {9}{2}\right ], \left [-\frac {3}{2}\right ], x\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.091 (sec). Leaf size: 71
DSolve[2*x^2*y''[x]-x*(1+2*x)*y'[x]+2*(4*x-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^{5/2} (4 (x-9) x+63) \left (32 c_2 e^x F\left (\sqrt {x}\right )+945 c_1\right )-32 c_2 e^x (x (x (x (2 x-17)+24)+6)+3)}{3780 \sqrt {x}} \\ \end{align*}