Internal problem ID [9516]
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]]
\[ \boxed {x^{2} y^{\prime \prime }+\left (-1+3 x \right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \frac {\left (c_{1} \operatorname {Ei}_{1}\left (-\frac {1}{x}\right )+c_{2} \right ) {\mathrm e}^{-\frac {1}{x}}}{x} \]
✓ Solution by Mathematica
Time used: 0.087 (sec). Leaf size: 27
DSolve[y[x] + (-1 + 3*x)*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-1/x} \left (c_1-c_2 \operatorname {ExpIntegralEi}\left (\frac {1}{x}\right )\right )}{x} \]