77.1.147 problem 173 (page 245)

Internal problem ID [18037]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 173 (page 245)
Date solved : Tuesday, January 28, 2025 at 11:23:18 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)-1/sqrt(x)*diff(y(x),x)+y(x)/(4*x^2)*(-8+sqrt(x)+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: 0.033 (sec). Leaf size: 30

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

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