Internal problem ID [8761]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1181.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime } x^{2}+\left (3 x -1\right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(x^2*diff(diff(y(x),x),x)+(3*x-1)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (c_{1} \expIntegral \left (1, -\frac {1}{x}\right )+c_{2}\right ) {\mathrm e}^{-\frac {1}{x}}}{x} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 27
DSolve[y[x] + (-1 + 3*x)*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-1/x} \left (c_1-c_2 \text {Ei}\left (\frac {1}{x}\right )\right )}{x} \\ \end{align*}