Internal problem ID [7218]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 498.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 55
dsolve((2*x^2+4*x+5)*diff(y(x),x$2)-20*(x+1)*diff(y(x),x)+60*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (-\frac {7}{4}+x^{5}+5 x^{4}+5 x^{3}-5 x^{2}-\frac {31}{4} x \right )+c_{2} \left (x^{6}+\frac {155}{8}-\frac {75}{2} x^{4}-100 x^{3}-\frac {225}{4} x^{2}+30 x \right ) \]
✓ Solution by Mathematica
Time used: 0.645 (sec). Leaf size: 73
DSolve[(2*x^2+4*x+5)*y''[x]-20*(x+1)*y'[x]+60*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {(2 x (x+2)+5)^{5/2} \left (c_1 \left (2 i x+\sqrt {6}+2 i\right )^6+4 c_2 (x+1) (2 x (x+2)-7) (2 x (x+2)+1)\right )}{(4 x (x+2)+10)^{5/2}} \\ \end{align*}