58.2.28 problem 28

Internal problem ID [9151]
Book : Second order enumerated odes
Section : section 2
Problem number : 28
Date solved : Monday, January 27, 2025 at 05:49:53 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 19

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)
 

\[ y = \frac {{\mathrm e}^{\sqrt {x}} \left (c_{2} x^{3}+c_{1} \right )}{x} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 30

DSolve[D[y[x],{x,2}]-1/x^(1/2)*D[y[x],x]+y[x]/(4*x^2)*(-8+x^(1/2)+x)==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{\sqrt {x}} \left (c_2 x^3+3 c_1\right )}{3 x} \]