Internal problem ID [6713]
Book: Second order enumerated odes
Section: section 2
Problem number: 28.
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: 0.016 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)-1/x^(1/2)*diff(y(x),x)+y(x)/(4*x^2)*(-8+x^(1/2)+x)=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: 0.017 (sec). Leaf size: 30
DSolve[y''[x]-1/x^(1/2)*y'[x]+y[x]/(4*x^2)*(-8+x^(1/2)+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*}