Internal problem ID [7478]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 760.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 50
dsolve((x^2-2*x+10)*diff(y(x),x$2)+x*diff(y(x),x)-4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (x^{2}-\frac {4}{3} x +5\right )+c_{2} \left (3 x -4\right ) \sqrt {x^{2}-2 x +10}\, \left (\frac {-x +1+3 i}{x -1+3 i}\right )^{\frac {i}{6}} \]
✓ Solution by Mathematica
Time used: 0.445 (sec). Leaf size: 90
DSolve[(x^2-2*x+10)*y''[x]+x*y'[x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} (3 x-4) \sqrt {(x-2) x+10} e^{-\frac {1}{3} \text {ArcTan}\left (\frac {x-1}{3}\right )} \left (c_2 \int _1^x\frac {9 e^{\frac {1}{3} \text {ArcTan}\left (\frac {1}{3} (K[1]-1)\right )}}{(4-3 K[1])^2 ((K[1]-2) K[1]+10)^{3/2}}dK[1]+c_1\right ) \\ \end{align*}