60.3.61 problem 1062

Internal problem ID [11071]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1062
Date solved : Monday, January 27, 2025 at 10:43:43 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: 0.008 (sec). Leaf size: 19

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)
 

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

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 30

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

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