Internal problem ID [8850]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1270.
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}+6 x +4\right ) y^{\prime \prime }+\left (10 x^{2}+21 x +8\right ) y^{\prime }+\left (12 x^{2}+17 x +8\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 54
dsolve((2*x^2+6*x+4)*diff(diff(y(x),x),x)+(10*x^2+21*x+8)*diff(y(x),x)+(12*x^2+17*x+8)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-2 x} \HeunC \left (-1, -\frac {5}{2}, 4, -\frac {7}{4}, \frac {7}{2}, -x -1\right ) \left (x +2\right )^{4}+c_{2} {\mathrm e}^{-2 x} \HeunC \left (-1, \frac {5}{2}, 4, -\frac {7}{4}, \frac {7}{2}, -x -1\right ) \left (x +1\right )^{\frac {5}{2}} \left (x +2\right )^{4} \]
✓ Solution by Mathematica
Time used: 2.42 (sec). Leaf size: 48
DSolve[(8 + 17*x + 12*x^2)*y[x] + (8 + 21*x + 10*x^2)*y'[x] + (4 + 6*x + 2*x^2)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-3 x} (x+2)^4 \left (c_2 \int _1^x\frac {e^{K[1]} (K[1]+1)^{3/2}}{(K[1]+2)^5}dK[1]+c_1\right ) \\ \end{align*}