Internal problem ID [9773]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1446.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+\frac {y^{\prime }}{x}+\frac {\left (x -1\right ) y}{x^{4}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve(diff(diff(y(x),x),x) = -1/x*diff(y(x),x)-(x-1)/x^4*y(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\frac {1}{x}} \left (c_{1} +\operatorname {expIntegral}_{1}\left (-\frac {2}{x}\right ) c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.077 (sec). Leaf size: 26
DSolve[y''[x] == -(((-1 + x)*y[x])/x^4) - y'[x]/x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-1/x} \left (c_1-c_2 \operatorname {ExpIntegralEi}\left (\frac {2}{x}\right )\right ) \]