Internal problem ID [8847]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1267.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime } x^{2}-\left (2 x^{2}+l -5 x \right ) y^{\prime }-\left (4 x -1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.017 (sec). Leaf size: 41
dsolve(2*x^2*diff(diff(y(x),x),x)-(2*x^2+l-5*x)*diff(y(x),x)-(4*x-1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (c_{1} \left (\int \frac {{\mathrm e}^{-x} {\mathrm e}^{\frac {l}{2 x}}}{2 x^{\frac {3}{2}}}d x \right )+c_{2}\right ) {\mathrm e}^{x} {\mathrm e}^{-\frac {l}{2 x}}}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.252 (sec). Leaf size: 135
DSolve[(1 - 4*x)*y[x] - (l - 5*x + 2*x^2)*y'[x] + 2*x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{x-\frac {l}{2 x}} \left (\frac {\sqrt {2 \pi } c_2 e^{-\sqrt {2} \sqrt {-l}} \left (e^{2 \sqrt {2} \sqrt {-l}} \text {Erfc}\left (\frac {\sqrt {-l}}{\sqrt {2} \sqrt {x}}+\sqrt {x}\right )+\text {Erfc}\left (\frac {\sqrt {2} \sqrt {-l}-2 x}{2 \sqrt {x}}\right )-2\right )}{\sqrt {-l}}+2 c_1\right )}{2 \sqrt {x}} \\ \end{align*}