59.1.576 problem 592

Internal problem ID [9748]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 592
Date solved : Monday, January 27, 2025 at 06:13:51 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} \left (1+x \right ) y^{\prime \prime }+8 x^{2} y^{\prime }+y \left (1+x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 19

dsolve(4*x^2*(1+x)*diff(y(x),x$2)+8*x^2*diff(y(x),x)+(1+x)*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 24

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

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