59.1.791 problem 813

Internal problem ID [9963]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 813
Date solved : Monday, January 27, 2025 at 06:16:12 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+\frac {2 y^{\prime }}{x}-\frac {2 y}{\left (1+x \right )^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 29

dsolve(diff(y(x),x$2)+2/x*diff(y(x),x)-2/(1+x)^2*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 34

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

\[ y(x)\to \frac {c_2 x \left (x^2+3 x+3\right )+3 c_1}{3 x (x+1)} \]