59.1.736 problem 755

Internal problem ID [9908]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 755
Date solved : Monday, January 27, 2025 at 06:15:39 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 28

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

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

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 37

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

\[ y(x)\to c_1 (x+1)-\frac {1}{2} c_2 ((x+1) \log (-x)-(x+1) \log (x+2)+2) \]