Internal problem ID [8642]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1062.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 23
dsolve(diff(diff(y(x),x),x)-diff(y(x),x)/x^(1/2)+1/4*(x+x^(1/2)-8)*y(x)/x^2=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} {\mathrm e}^{\sqrt {x}}}{x}+c_{2} {\mathrm e}^{\sqrt {x}} x^{2} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 30
DSolve[((-8 + Sqrt[x] + x)*y[x])/(4*x^2) - y'[x]/Sqrt[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{\sqrt {x}} \left (c_2 x^3+3 c_1\right )}{3 x} \\ \end{align*}