Internal problem ID [8745]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1165.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+\left (x +a \right ) y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 19
dsolve(x^2*diff(diff(y(x),x),x)+(x+a)*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \left (x +a \right ) c_{1}+c_{2} {\mathrm e}^{\frac {a}{x}} x \]
✓ Solution by Mathematica
Time used: 0.083 (sec). Leaf size: 26
DSolve[-y[x] + (a + x)*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 (a+x)}{a^2}+c_1 x e^{a/x} \\ \end{align*}