Internal problem ID [8767]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1187.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {y^{\prime \prime } x^{2}+a x y^{\prime }+b y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 53
dsolve(x^2*diff(diff(y(x),x),x)+a*x*diff(y(x),x)+b*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{-\frac {a}{2}+\frac {1}{2}+\frac {\sqrt {a^{2}-2 a -4 b +1}}{2}}+c_{2} x^{-\frac {a}{2}+\frac {1}{2}-\frac {\sqrt {a^{2}-2 a -4 b +1}}{2}} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 53
DSolve[b*y[x] + a*x*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^{\frac {1}{2} \left (-\sqrt {(a-1)^2-4 b}-a+1\right )} \left (c_2 x^{\sqrt {(a-1)^2-4 b}}+c_1\right ) \\ \end{align*}